Mamihlapinatapai: Games People (Might) Play.

Dwyer, Peter D.

ABSTRACT

With a focus on Melanesia, game theory is used to model the logical structure of strategic interactions between actors who engage in exchange transactions and to identify paradoxes, opportunities and uncertainties that confront those actors. It is argued that these exchanges are of three types which are named sharing, barter-trade and prestige-service. The first has the form of the classic game known as Prisoner's Dilemma and the expectation of non-cooperation inherent in this game is resolved by trust. The second has the form of a game known as Chicken and the high risk inherent in this game is resolved by social manipulations that transform the payoff structure into Prisoner's Dilemma. The third is always an n-person game. It has the form of a prestige game with an unconventional logical structure that is contingent on the existence of a parallel set of service games, each having the form of Chicken. The paper concludes by attempting to restore some realism to models that were over-simplified abstractions. Some reinterpretations of conventional understandings are suggested.

INTRODUCTION

Mamihlapinatapai is a Tierra del Fuegian word meaning 'looking at each other hoping that either will offer to do something which both parties desire but are unwilling to do' (Matthews 1992:148). I take the word, metaphorically, to convey the sense that people often engage in strategic interactions and often know that they do. More precisely, perhaps, the word captures some essence of the fact that the logical structure of potential interactions may predispose to outcomes that are neither desired nor desirable and actors may strive to manipulate that structure into more acceptable forms. The contrast here is that which exists between 'logical logic, which can deduce rational action from the explicit, explicitly controlled and systematized principles of an axiomatics' and the practical logic of lived experience (Bourdieu 1990:102). Bourdieu wrote of the participants to an interaction as 'strategists', of outcomes in terms of changes to various kinds of 'capital' and of the interactions themselves as 'games'.

The notion of 'games', in at least a figurative sense, appears relatively often in the anthropological literature (e.g. L[acute{e}]vi-Strauss 1966:30-2; Strathern 1971:10-4; Weiner 1977; Gell 1992a:263-85; Zimmer-Tamakoshi 1997) and, in a literal sense, has received attention in, for example, explorations of the post-contact emergence, and role, of card games among some Papua New Guineans and Australians (Maclean 1984; Zimmer 1986, 1987; Goodale 1987; Sexton 1987). However, in recent literature, with few exceptions, sociocultural anthropologists have seldom drawn on game theory despite the fact that this deals explicitly with the formal structure and possible competitive and cooperative outcomes of strategic interactions between actors (Colman 1995). This current resistance to game theory may be traced, in part, to dissatisfaction with assumptions of, for example, rational decision-making and stasis that seemed to be implicit in early studies (e.g. Barth 1959; Kapferer 1976) and, as well, to changing perspec tives that sought to avoid both connotations of 'strategic intention' and the prioritization of theory in explanations of human behaviour (Bourdieu 1998:81). But, in as much as these reasons do contribute to an anthropological distaste for game theory, that distaste may be unwarranted. Game theoretical models predict outcomes that are expected to follow when actors behave in particular ways in a context of the behaviour of other actors; there is no necessary assumption of intentionality, the strategies available to or adopted by an actor may arise from, as Bourdieu would have it, 'a feel for the game' rather than from calculation.

Colman and Wilson (1997:25) wrote that game theoretical models are abstract idealizations of 'phenomena', that deductions arising from those models are true only with reference to the models themselves, and that the extent to which a model 'corresponds to the original phenomenon is always a matter of judgement and empirical evidence'. The rationality assumed by game theoretical models is inherent in the formal structure of those models, it is not necessarily inherent in actors who confront and must resolve situations that are constructed in this way. That is, for both analysts and actors there may be a disjunction between the rules of the game (logical logic) and adjustments made in the light of those rules (practical logic). To this extent, the anthropological value of game theoretical analysis may reside in its potential to reveal the formal or logical structure of particular strategic interactions, to detect similarities and differences among apparently related strategic interactions, and to make explicit the paradoxes, opportunities and uncertainties that confront, and must be resolved by, actors who engage in strategic interactions. Stated simply, game theoretical analysis may reveal the structure of problems that people are called upon to solve. But this simple statement contrasts my approach with that of many biologists and biologically-inclined anthropologists who assert that, rather than merely clarifying the formal structure of problems, game theoretical models may yield solutions to those problems (e.g. Maynard Smith 1982; Badcock 1991; Hawkes 1992; No[ddot{e}] and Hammerstein 1994; Dugatkin 1996; Ridley 1997). The biological approach is further confused by the fact, that analysts conflate the use of particular models to explore questions concerning the reproduction of form and the legitimate, but logically distinct, use of the same models to explore questions concerning the origin of form. [1] In this article my explanatory aim concerns only the reproduction of systems of relations, the place of game theory in exploring interactions that have economic, social and political dimensions. But, in as much as I move from models to ethnographic fact, it is clear that my approach does prioritize theory and encounters problems that, so often, are associated with this; in particular, perhaps, the problems that sequential acts appear as synchronous and, hence, that the potential for change is disguised. [2] Change that arises in the circumstance of context-dependent reproduction may be accommodated within game theoretical models but those models are silent with respect to agency and, to this extent, do not address questions of transformation.

THE ETHNOGRAPHIC PROBLEM

In a recent article G[ddot{o}]rlich (1998a) made explicit use of game theory to address a problem concerning Melanesian exchange. He argued that the logical structure of barter-trade is that of the classic and well known game named Prisoner's Dilemma. The paradoxical expectation derived from Prisoner's Dilemma is that self-interested (rational) actors will choose the lower payoff derived from mutual defection (i.e. reneging on a reciprocal exchange) over the higher payoff derived from mutual cooperation (i.e. proceeding with a reciprocal exchange). G[ddot{o}]rlich (1998a) discussed ways in which actors might overcome this dilemma by constructing social relations. In another article he again prioritized Prisoner's Dilemma in analysing the structure of ceremonial gift exchange in Melanesia (1998b). In both articles he sought rapprochement between the contrary opinions concerning the nature of gift exchange vis-[grave{a}]-vis barter-trade (or commodity exchange) that were put forward by Gell (1992b) and Strather n (1992).

Gorlich (1998a) correctly observed tat barter-trade may be often an insecure or dangerous enterprise. Game theorists do not, however, consider Prisoner's Dilemma to be inherently dangerous; rather, it is a game known as Chicken that stands out as a high risk or dangerous game (Colman 1995:11 1-5). [3] The logical structure of these two mixed-motive games is different. In this article, I argue tat the formal structure of barter-trade is best interpreted as a game of Chicken and that, in as much as risk is unacceptably high, actors respond by manipulations that alter the structure of the game to that of Prisoner's Dilemma. But the paradox inherent in the latter game remains, and, with human actors, is usually and ultimately resolved by recourse to trust.

To some extent I shall be arguing that, with respect to barter-trade, Gorlich (1998a) reached the right answer for the wrong reasons. At the same time, however, he left too much out, for his own answer to be acceptable. I shall show, for example, that in some circumstances the operative exchange game is in fact Chicken and argue that it is trust which sets the stage for this game. I shall show also that Prisoner's Dilemma is an inappropriate model for the analysis of ceremonial gift exchange. In what follows I first diagnose key variables to be entered into a game theoretical analysis of exchange. I then model several simple situations that turn upon distinctions in economic value (equivalent and non-equivalent), temporality (immediate and delayed) and context (intra- and inter-regional). I identify the logical structure and theoretically expected outcomes of these situations and discuss ways in which actors may respond to those structures and expectations. Finally, with specific reference to Melanesian syst ems of exchange, I attempt to restore some realism to models that were deliberately and necessarily over-simplified abstractions.

THE VARIABLES

In the analyses that follow payoffs to actors are assessed in terms of four variables that are intrinsic to the structure of an exchange transaction. Three of these are labelled economic capital, social capital and political capital though the meanings I give these terms are specific to this article and not entirely congruent with the variety of meanings encountered elsewhere. [4] The fourth variable, which is labelled 'risk', arises in the context of several possible sources of asymmetry; it influences the likelihood of conflict and is experienced by one or both actors as a cost. I elaborate on each of these variables below.

For each actor the economic capital derived from an exchange of items arises from the difference between the potential economic value, to that actor, of the item received and the potential economic value, to the same actor, of the item given. Economic value is always assessed from the perspective of a particular actor. [5] But, of course, the transaction may not run to completion; one or other, or both, actors may renege on the exchange. Thus, changes to the economic capital of Actor 1 arising from a single act of exchange may be coded as [E.sub.1r] where the actor receives but does not give, [[E.sub.1r] - [E.sub.1g] where the actor both receives and gives, 0 where both actors renege and -[E.sub.1g] where the actor gives but does not receive. Hereafter, [[E.sub.1r] - [E.sub.1g]] and [[E.sub.2r] - [E.sub.2g]] are recoded as [E.sub.1] and [E.sub.2] depending on the actor.

Acts of exchange carry the potential to affirm and establish relationships between the actors themselves. Thus, in the social (or, perhaps, moral) universe within which two actors are embedded the transfer of an item from one to the other can be taken as a statement by the former of a desired relationship with the latter. In a context of sharing, for example, an actor who gives to another has identified that particular other as 'worthy' in relation to all others with whom he or she did not share. Milner (1994) and Reuter (1999), writing of India and Bali, treated such bestowal of 'worth', derived through expressions of social approval, as one variant of 'non-material (symbolic) capital'. Here it is regarded as social capital and the contexts of bestowal are taken to be broader than Milner and Reuter considered. In much of the Melanesian literature sharing is represented as a moral imperative and, in contrast to my assessment, as value neutral and unproblematic; it is often not considered in analyses of excha nge (e.g. Gell 1992b:151; Kelly 1993:74-5). In the models that follow the value of social capital is assumed to be symmetrical; that is, on the proviso that reciprocity occurs, both actors gain to the same extent. In fact, this need not be the case, but the simplifying assumption should have little impact on arguments developed here. In those models social capital is coded as S.

Acts of exchange also carry the potential for actors to employ the items exchanged as a means of affirming or establishing relationships with third parties. This may be achieved only where one actor holds exchange items in fact or in trust beyond accepted expectations concerning delays in reciprocation or has alternate means, not available to the exchange partner, to employ those items in transactions with third parties. It is the bias in extra-dyadic opportunities available to an actor -- opportunities made possible by the dyadic interaction -- that qualifies as political capital. In the models that follow the gain in political capital relative to that already held is coded as [P.sub.1] and [P.sub.2] depending on the actor.

Under the foregoing definitions both social capital and political capital accrue to the recipient in an exchange transaction. In the first case both actors in a dyadic transaction gain in the circumstance of reciprocation. In the second case one actor in a dyadic transaction gains only at the expense of the other. At first sight, therefore, my definitions may appear to be at odds with conventional wisdom in ignoring possible gains to donors. Gregory (1982:47-8), for example, wrote that the 'exchange of like-for-like' establishes 'an unequal relationship of domination between the transactors' that bestows 'some kind of superiority' upon the giver. In Melanesian studies the implied 'superiority' arises when one actor, through apparent acts of generosity, places an exchange partner in a position of indebtedness and accrues prestige or some other form of what might be called 'cultural capital'. Milner (ibid.) and Reuter (ibid.) write, more generally, of actors negotiating access to status through strategic engag ement with members of their own or other status groups; they regard the accrual of approval by these means as another variant of 'non-material (symbolic) capital'. They recognise, as I do, circumstances in which both recipients and donors may accrue non-material benefits from an exchange but differ from me in collapsing these forms of capital under a single label. In the models developed below it is shown that accrual of prestige is contingent upon activation of accumulated political capital (see Model 4). That is, a recipient who delays reciprocation, accrues political capital, and uses this to create indebtuess with third pates via apparent acts of generosity, does indeed achieve 'some kind of superiority' vis-[grave{a}]-vis those third parties. Prestige is an outcome of a particular class of exchange transactions; it is not a variable that needs be entered into the payoff structure of those transactions.

The fourth variable entered into the models that follow concerns the potential for collapse of the exchange relationship. As the magnitude of [[E.sub.1] - [E.sub.2]] increases so will the potential for conflict and one or both actors will experience the exchange transaction as increasingly risky. Recall that [[E.sub.1] - [E.sub.2]] is a difference between differences; it may be influenced by either discounting or inflationary effects and, thus, may be substantial in dyadic transactions. The potential for conflict will also increase as the magnitude of the difference between two actors in their accumulated political capital increases; the value of any increment or loss in political capital to an actor will depend on the amount already held. Finally, and in line with G[ddot{o}]rlich's (1998a:298) comments concerning barter-trade, risk is entailed in contexts where one or other of the participants in an act of exchange has travelled beyond his or her home territory. Here, risk is likely to be greater for the ac tor who is not located on home territory. Thus, risk is associated with asymmetries in both economic and political capital and in the geographic context of exchange. In all cases the impact of risk will be experienced as a cost that itself varies with the magnitude of those asymmetries and, ultimately, influences the probability that an actor may be excluded from participation in the exchange network. In the models that follow the impact of risk is coded as -[R.sub.1] and -[R.sub.2] depending on the actor; it is always felt as a cost and, hence, is shown as negative. In those models I consider only sources of risk that arise from within the logical structure of the exchange; in discussion I comment on some sources of risk, and associated responses, that may be extrinsic to that structure.

The variables identified above are assembled in Table 1 as a generalized matrix that records potential payoffs to both actors. The terms cooperation and defection are standard usage in game theory; for present purposes the former stands for giving (and reciprocation) and the latter for reneging. In the table, payoffs to Actor 1 are unbracketed, those to Actor 2 are bracketed.

If Actor 2 cooperates the potential payoffs to Actor 1 vary according to whether he or she reciprocates or reneges. In the first case, the payoff may be represented in terms of changes to economic and social capital; in the second case, the payoff may be represented in terms of changes to economic, social and political capital. (With respect to a single move an actor who responds to cooperation by defecting incurs no costs unless an imbalance in economic capital is to his or her disadvantage. Defection may, however, incur subsequent costs that are contingent upon responses made by the initially cooperating actor.) If Actor 2 defects, but Actor 1 cooperates, then the potential payoff to the latter may be represented in terms of a change (in fact a reduction) to economic capital. Finally, I argued above that risk increases as asymmetries of payoff or context emerge within the structure of the exchange. As risk increases so too does the likelihood that an intended exchange will collapse and that an actor is exc luded from the exchange network. Thus, as shown in Table 1, the impact of risk contributes as a cost to the payoff of an actor in the circumstance of mutual defection. It is only in this circumstance, and where the magnitude of cost relative to other payoff variables exceeds some limiting threshold, that the penalty arising from mutual defection will be greater than the penalty arising from cooperating in response to defection. [6]

In different circumstances each of the variables assembled in Table 1 will be more or less important in contributing to the actual payoff accruing to a particular actor. Below I explore some simple models that reveal both how the logical structure of exchange may itself alter with circumstance and how actors might be expected to accommodate to the paradoxes, opportunities or uncertainties inherent in those structures. Thus, in proposing the models I strive for generality and precision and, in accommodating people to those models, I proceed to sacrifice both the former as I strive for realism (cf. Levins 1966).

MODELLING EXCHANGE

I commence by exploring exchanges that are intraregional; that is, the participating actors are members of a relatively localized network of individuals. Exchanges that are immediate are examined briefly before turning to those in which a delay occurs between giving and receiving. With intraregional delayed exchanges I first examine situations in which economic and social but not political capital are important, secondly, situations in which all forms of capital are important and, thirdly, situations in which political capital is activated in the interests of acquiring prestige. Finally, I turn to the type of exchange transaction that was examined by Gorlich (1998a); interregional exchanges which may be either immediate or delayed.

Intraregional, immediate exchange (Model 1)

Here, the modelled exchange is envisaged as occurring between actors within a regularly interacting network. Given that the intended exchange is literally immediate there are only two possible outcomes, either both actors cooperate or both actors defect. The only variables relevant to the payoff matrix are [E.sub.1] ([E.sub.2]) and S (Table 2).

Under this model, if the items exchanged are of equivalent economic value then both [E.sub.1] and [E.sub.2] equal zero. The exchange is predicted to proceed on the proviso that the increment in social capital is judged to be satisfactory by both parties (Model 1A). If the items exchanged differ in economic value then the exchange is predicted to proceed on the proviso that both [E.sub.1] and [E.sub.2] are positive; that is, on the proviso that each actor accords higher value to the item held by the other than to the item held by self (Model 1B; expected outcomes could be rendered more complex by allowing that actors differed in the ways in which they weighted economic and social capital). Model 1B would fit situations of intra-community barter in which, for a given actor, the marginal value of an item of one kind decreases as the number of items of that kind held by that actor increases. In neither of these cases does the logic of the game qualify as mixed-motive or implicate strategic choices though, in pra ctice, actors may attempt to manipulate economic value to their own advantage. (Note that Model 1B might be elaborated to investigate markets and bargaining; these sorts of transactions are outside the brief of the present article.)

Exchange that is literally immediate may be ethnographically relatively uncommon. [7] Delayed exchange is more usual but is, by no means, a unitary phenomenon. Rather, it qualifies as an anthropological b[hat{e}]te noire, resisting unambiguous categorization as it affords tempting dichotomies: generalized versus balanced, non-reciprocal versus reciprocal, use-value versus exchange-value, moral versus social, secular/commodity versus ceremonial/gift, service versus gift/commodity (e.g. Sahlins 1974; Gregory 1982; Parry 1986; Gell 1992b; Strathern 1992). Perhaps the primary contrast common to, or intended by, these dichotomies is that between exchanges in which payoffs hold relevance only with respect to a pair of actors (who could be individuals or groups) and exchanges in which the payoffs arising from a dyadic interaction may, in some way, extend to engagement with third parties. A second, though less satisfactory, contrast might be between exchanges in which reciprocation closes an interaction by terminati ng debt (exchanges embedded in B-time, Gell 1992a:275-85) and exchanges in which reciprocation continues an interaction by creating debt (exchanges embedded in A-time, ibid.). With reference to at least the first possibility, and the payoff variables I am employing, the contrast would be between delayed exchanges which do not implicate political capital

(see Model 2) and delayed exchanges which do implicate political capital (see Model 3).

Intraregional, delayed exchange without politics (Model 2)

The modelled exchange is again envisaged as occurring between actors within a regularly interacting network. Relevant variables are economic and social capital. The payoff matrix is shown as Table 3; actual payoffs appear on the left and ranked payoffs, from a high of 4 to a low of 1, appear on the right. It is assumed that items exchanged are of equivalent economic value and, hence, that both [E.sub.1] and [E.sub.2] equal zero. The conclusions would not be altered if [E.sub.1] and [E.sub.2] were greater than zero but, to the extent that one or both was less than zero, the exchange would be less likely to proceed.

The ranked payoffs in Table 3 reveal that the structure of the payoff matrix is that of a Prisoner's Dilemma. As noted earlier, the logic of this dilemma is that self-interested actors are expected to choose mutual defection when, in fact, they would receive a higher payoff from choosing mutual cooperation. Each actor will always do best by defecting, whatever the other actor does; that is, by defecting, Actor 1 obtains a payoff of rank 4, rather than rank 3, if Actor 2 cooperates and a payoff of rank 2, rather than rank 1, if Actor 2 defects.

The logical expectation of outcome that is implicit in the payoff matrix of Prisoner's Dilemma is, however, at odds with the cooperative behaviour that is often observed in real situations. In dyadic transactions this discrepancy between expectation and observation may be theoretically resolved in two ways. First, mutual cooperation can arise and be stable for long periods where actors engage in transactions on multiple and indefinite occasions and operate according to a rule under which each cooperates on the first move and, thereafter, mimics the choice of the other actor. That is, where a one-shot Prisoner's Dilemma is expected to lead to mutual defection, a repeated Prisoner's Dilemma can yield mutual cooperation. Biologists name the rule tit-for-tat and, with reference to actors who are not biological kin, describe the behaviour that results as reciprocal altruism (Wilkinson 1984; Hawkes 1992:277-9;Colman 1995:144-9). [8] Secondly, the payoff values of a Prisoner's Dilemma may sometimes be partitioned t o reveal how different components are distributed among the two actors. This is illustrated in Table 4 which shows that the partitioned payoffs from a cooperating move by an actor are -[E.sub.1g]to self and [E.sub.1r] +S (i.e. identical with ([E.sub.2r]+S) to exchange partner and from a defecting move are zero to both self and exchange partner. In this circumstance of complete information about the structure of the payoff matrix an actor may know that the most favourable outcome from repeated encounters arises from mutual cooperation. This outcome may be then expected under a proviso that both actors consider that their partner also has complete information (Colman 1995:154-60); in a one-shot game at least, and as verified experimentally, there remains a requirement that trust is established (Frank et al. 1993).

Boyd and Richerson (1988) have shown mathematically that, as the number of players in an n-person repeated Prisoner's Dilemma increases, mutual cooperation is less likely to be stable. (Note that an n-person game is one in which multiple actors interact as dyads; there is no implication that the outcome for an actor with respect to any particular dyad influences that actor's interaction with a third party.) Boyd and Richerson's modelling exercise made no allowance for the possibilities that actors who defected might be punished by all others withholding cooperation or that actors in the group were a priori associated within some kind of network. They considered that these factors, alone or together, might increase the theoretical likelihood of mutual cooperation. Both possibilities apply to the situation that I have modelled. Further, both connect with the importance of trust either in the sense that withholding cooperation may be understood as a penalty for breaking trust or in the sense that trust will be inherent in a viable and sustaining social network.

Both in theory and in practice, with two-person and with n-person games, resolution of the expectation of mutual defection that is inherent in the logic of Prisoner's Dilemma ultimately requires that human actors establish some measure of trust with exchange partners. Where a payoff matrix may be disaggregated as shown in Table 4 there may be a rational basis for trust. But, interestingly, to the extent that trust is established within a group of actors it provides opportunities that may be exploited by particular actors. For the time and to the extent that an actor holds, in fact or in trust, a disproportionate share of exchange items these may be employed to establish prestige through acts of generosity (and, hence, the creation of indebtedness) directed toward other actors. In a context of delayed exchange trust provides opportunities to accrue political capital and this, in turn, may alter the logical structure of the game.

Intraregional, delayed exchange with politics (Model 3)

The modelled exchange is again envisaged as occurring between actors within a regularly interacting network. Economic, social and political capital are all relevant and costs associated with the impact of risk play a part to the extent that [[P.sub.1] - [P.sub.2]] is not equal to zero. The last variable refers to the differential gain in political capital between actors. As stated earlier a differential in the political capital of two actors arises where one of those actors holds exchange items in fact or in trust beyond accepted expectations concerning delays in reciprocation or has alternate means, not available to the exchange partner, to employ those items in transactions with third parties. At this juncture there is no reference to ways in which either actor may activate political capital in interactions with third parties; that is, the present model is concerned only with the acquisition of political capital. Again, I assume that items exchanged are of equivalent economic value and, hence, that both [E.sub.1] and [E.sub.2] equal zero. [9] The payoff matrix is shown as Table 5.

For Actor 1 the payoffs shown in Table 5 may be ranked from highest (4) to lowest (1) only after it is determined whether [R.sub.1] is less than or greater than [E.sub.1g] if [R.sub.1] is less than [E.sub.1g] then the distribution of ranks corresponds to that shown in Table 3, the game is Prisoner's Dilemma and the previous discussion of options and alternatives remains relevant (i.e. Model 2). This, in fact, is the likely outcome of a two-person interaction because a disadvantaged actor would be expected to cease cooperating when the differential in economic (and political) capital was relatively low. But in an n-person game an actor who was perceived as trustworthy could accumulate high political capital relative to each of many others despite the fact that, for each dyad, the differential in economic capital was relatively low. In this circumstance, the outcome of a dyadic transaction would be that the relative gain in political capital to a recipient who already held high political capital would be less than the relative loss to a donor with low political capital. As the magnitude of [[P.sub.1] - [P.sub.2]] increased so too would costs arising from the impact of risk and, at the point where [R.sub.1] was greater than [E.sub.1g]' the distribution of ranks would alter (i.e. the ranks of 2 and 1 shown in Table 3 would switch cells such that t [greater than] r [greater than] s [greater than] p), the game would now be Chicken and the expected behaviour of actors would change (cf. Hawkes 1992:280-3).

Thus, in the context of an n-person game, in which trust facilitates emergence of a substantial differential in political capital, the structure of the game alters from that of a relatively benign Prisoner's Dilemma to a potentially dangerous game of Chicken. And, in an n-person game of Chicken, equilibrium may be achieved if either all actors choose to cooperate on x-percent of their moves and defect on the remainder or x-percent of actors choose to always cooperate and the remainder choose to always defect (Dawkins 1976:74-80; Hawkes ibid.). This is the Nash equilibrium of game theory or the 'ecologically secure solution' of biological approaches (Colman 1995:276-83; see Note 1). For the model under consideration the value of x increases and, hence, the expected proportion of defection decreases as the magnitude of R increases (Fig. 1). In the more likely circumstance that particular actors emerge as consistent defectors they may be envisaged as entrepreneurs who exploit the trust inherent in one set of re lationships to accrue political capital that they then use to establish prestige within a more far-reaching set of relationships.

Activating political capital (Model 4)

Model 3 is concerned with ways in which political capital may be financed (or serviced) but is not itself cognisant of the exchanges that may occur with third parties by actors who have accumulated sufficiently high political capital. Activation and maintenance of these exchanges is, however, necessary to establishing the prestige that is made possible by political capital. In the simplest scenario it would be expected that actors with high political capital would enter into dyadic exchange relationships with others who were similarly placed. For each actor the aim would be to accrue prestige through, first, acts of generosity that established indebtedness and, secondly, having the where-with-all to remain in the game and, hence, the opportunity to be generous. The payoff matrix for Model 4 is shown as Table 6; I assume that social capital, as defined above, is not of primary interest to either actor and that items exchanged are of equivalent economic value and, hence, both [E.sub.1] and [E.sub.2] equal zero. Actor 1 receives the highest payoff by responding to reneging (defection) by giving (cooperation) and the lowest payoff by responding to defection by defection and, thereby, being excluded from access to prestige. Under this model, exclusion qualifies as a cost, analogous to that arising from the impact of risk, and is coded as '-[R.sub.1]' and '-[R.sub.2]' depending on the actor. Here it is participation or non-participation in the game that constitutes the asymmetry which contributes to that cost.

The payoff matrix shown in Table 6 does not qualify as a conventional mixed-motive strategic game for the simple reason that the rationality assumed in those games does not allow for the possibility that an actor might 'win' by 'losing'. In an important sense, therefore, the logical form of the game is a construction of the players themselves and the communities to which they belong. From the table the relative ranks of payoffs to an actor from mutual cooperation, retaliative cooperation-defection and mutual defection may be estimated as 3, 3 [i.e. (2 + 4)/2] and 1. The expected outcome would be that actors opt for mutual cooperation; that is, an actor who always cooperated could never be beaten by the other actor. But this does not provide a basis for the asymmetry that provides the best route to prestige. Once more, actors must manipulate each other to their own ends. In a context of multiple trusted and trusting partners, and a favourable servicing network, each actor may manipulate (coerce) creditors and debtors so that he or she is seen to be frequently generous. Retaliative cooperation-defection, grounded in a species of coercive-trust, is the strategic fiction -- the practical logic -- that underwrites prestige. Only in this circumstance may an actor publically demonstrate superiority -- that is, the creation of indebtedness -- vis-[acute{a}]-vis a particular exchange partner while, in fact, standing in a relationship of indebtedness to other participants in the game. As the payoff matrix shown above implies, retaliative cooperation-defection entails continual circulation of the actual items (or their equivalents) that are exchanged. But the important insights from this analysis are, first, that the game which provides access to prestige is ultimately contingent upon the parallel existence of games of Chicken and, secondly, that, for particular actors, continued participation in the former requires that the risk inherent in the latter does not exceed a threshold of unacceptable cost to other actors. I sha ll return to these matters in discussion. [10]

Interregional exchange (Model 5)

In the first instance the modelled exchange is envisaged as occurring between actors who, otherwise, are members of distinct networks and as entailing travel beyond the home territory by at least one of those actors. These conditions draw attention to the importance of two variables in contributing to the payoffs of actors. First, the geographic context in which the exchange takes place is itself inherently risky. Secondly, where different kinds of items are exchanged, one or the other actor may be tempted to increase the magnitude of the difference between [E.sub.1] and [E.sub.2] via inflation and in his or her own favour. This too will increase risk. For the minimal conditions identified here changes in social and political capital do not contribute to the payoffs of the two actors considered. The payoff matrix is shown as Table 7; Actors 1 and 2 are distinguished as being located off and on their home territory respectively.

Under the terms of this model it is likely that the magnitude of the geographically-mediated difference between [R.sub.1] and [R.sub.2] is large and is experienced as a high potential cost by Actor 1. Actor 1 may similarly be more vulnerable than Actor 2 to inflation, which would further increase the differential in risk. For Actor 1, therefore, the logical structure of the payoff matrix is likely to qualify as a very dangerous game of Chicken, a game in which the odds are stacked in favour of the other actor. To the extent that the potential costs to Actor 1 are unacceptable the exchange may proceed only if arrangements are put in place that directly or indirectly reduce either [R.sub.1] and [R.sub.2] or the magnitude of the difference between them. This might be achieved by increasing the potential costs experienced by Actor 2, by activating social ties between the participating actors or both. Potential costs to Actor 2 could be increased, and hence the difference between [R.sub.1] and [R.sub.2] reduced, by a requirement that Actor 2 travelled to the territory of Actor 1 to complete the exchange (i.e. to either give or receive a reciprocal exchange item). This is not uncommon in barter-trade (e.g. Malinowski 1922). [R.sub.1] and [R.sub.2] could be also indirectly reduced by a variety of mechanisms including the formation of lasting partnerships that heighten prospects for trust, contracting intergroup alliances by way of marriage arrangements that link the traders as kin, employing experienced intermediaries who have established a basis for trust and, with arrangements of these kinds in place, conducting barter-trade in the shadow of socially-motivated exchange.

It is important to note that, with the exception of enforcing geographic symmetry, none of the arrangements listed above is inherent in the logical structure of the game itself. But, in as much as they have the outcome that risk is reduced to the point where [R.sub.1] (and [R.sub.2]) is less than [E.sub.1g] (and [E.sub.2g]), and social capital is introduced as a relevant variable, then the structure of the game has shifted from that of Chicken to Prisoner's Dilemma (Model 2).

STEPS TOWARDS REALISM

Models derived from game theory cannot explain systems of exchange. At best they can reveal the logical structure of situations that entail strategic encounters between actors and, in as much as they achieve this, also reveal potentially problematic or paradoxical outcomes that require resolution. The models themselves will seldom contain the information needed to resolve those problems or paradoxes. The task now, therefore, is to explore some implications of models developed in this article for situations that more closely approximate ethnographic reality.

The strategic interactions I have modelled may be represented as three distinct games. The first two are relatively simple. They are 'sharing' that has the logical structure of Prisoner's Dilemma (Model 2, Table 3) and 'barter-trade' that has the logical structure of Chicken (Model 5, Table 7). The third is complex in that it embeds a set of games that takes one form within a game of another form. This is 'prestige-service' in which a prestige game that has an unconventional logical structure (Model 4, Table 6) is contingent upon the existence of a set of companion service games that have the logical structure of Chicken (Model 3, Table 5). The distinction between the sharing and prestige games is important and may be reduced to an understanding that in the former 'profit' is good while in the latter 'loss' is good. The logic of the latter game requires that there are multiple players and that exchange items (or their equivalents) are kept in circulation; the logic of the former game does not have these requ irements. These differences, which have emerged from the modelling exercise, reinforce the distinction I have drawn between social and political capital on the one hand and between these forms of capital and the acquisition of prestige on the other. The prestige-game, in which ceremony often accords high visibility, has been often prioritized as a primary mode of exchange by ethnographers. It is important to note also that in different situations particular actors are likely to engage in different sorts of games; indeed, they may well be simultaneously engaged in different games with the same other individual. In what follows my references to this matter will be tangential.

The sharing game as modelled here entails strategic interactions in which economic and social capital are important and resolution of the theoretically expected outcome of mutual defection is achieved by recourse to trust established between participating actors. The game is not inherently risky though there are situations in which sources of risk, arising outside the given structure, may impact on the game. This occurs, for example, among Kubo people of the interior lowlands of Papua New Guinea where an abiding concern with intracommunity sorcery may be understood to continually erode social capital and where the response is an extraordinarily high rate of sharing of raw and cooked, plant and animal, food -- often, for a pair of individuals, on the same day and of the same food-stuffs (Dwyer and Minnegal 1992). It should be understood also that the payoffs that accrue from dyadic sharing transactions with multiple individuals may be sufficient to accommodate some nonreciprocators within a network of recipro cators. That is, average payoffs to actors may hold more significance than an expectation that all dyadic interactions result in favourable outcomes. In a community-based repeated game of Prisoner's Dilemma there may be room for individuals who free-ride for a time and move on before reciprocation is demanded. In game theory this strategy is known as Rover (Dugatkin and Wilson 1991; Houston 1993) and, among Kubo, is adopted by some bachelors (Dwyer and Minnegal 1997:105; this paper provides a detailed example of the sharing game based on an analysis of differentials in the production of sago flour).

The barter-trade game as modelled here entails strategic interactions in which potential differentials in economic capital and the impact of geographically-mediated risk yield an inherently dangerous structure that is ultimately resolved by arrangements that either render risk symmetrical, link participants within a kinship or kinship-like network or both. On either count manipulations by participants have the effect that payoffs associated with cooperation and defection are altered and the logical structure of the game shifts from that of Chicken to that of Prisoner's Dilemma. At base, therefore, people who engage in barter-trade decline to operate within the terms of reference of the transparent logic of the game. Rather, they strive to transform the given terms of reference to achieve and maintain, in fact or appearance, a transactional structure like that of sharing, of mutual cooperation that is grounded in trust (Henley 1990:315-6). The temptation to defect from this latter structure, to cheat trading partners by inflation or by delaying a reciprocal exchange beyond conventionally accepted limits, can be tempered only by an understanding that this will return the game to its initial and dangerous form. The Dobuan notion of wabuwabu, expressed as an attractive but perhaps seldom implemented ideal of 'profiteering by cheating', illustrates nicely that participants are alert to both the logical and practical logic of their endeavours (Fortune 1963:216-8; see also Gell 1992a:280-2). [11]

The sorts of arrangements I have identified in relation to barter-trade are those to which G[ddot{o}]rlich (1998a) drew attention though, for reasons connected with his particular ethnographic focus, he placed less emphasis than I would upon the strategy of reciprocal travel. Those sorts of arrangements were also summarized succinctly by Sahlins (1974:201). But G[ddot{o}]rlich did not recognise that the logic of the game, prior to manipulation by the actors themselves, was that of a very dangerous game of Chicken or that it was for this reason that manipulation was necessary; his illustrative payoff matrix did not allow for the cost that would be entailed in 'losing all one's goods, or even one's own life' in the course of the transaction (ibid.:298-9). The manipulations he considered to be important served, first, to transform the barter-trade game into a sharing game and, only secondly, to establish conditions whereby trust could provide a resolution to the paradox of mutual defection inherent in the latte r game.

The prestige-service game as modelled here is, of course, two games rolled into one with the latter providing both the finance and the guarantee for the former. In the latter game some actors exploit the trust of others to delay returns and accrue political capital. In the former game those actors (entrepreneurs) activate political capital by redirecting items, or their equivalents, that are held in trust to establish indebtedness with third parties. To the extent that they are successful, entrepreneurs may be accorded prestige by members of both networks within which they interact. At the same time, however, they are playing a risky game. If the differential in political capital that arises within the service network is low then many actors may engage in 'low level' entrepreneurial behaviour. But in as much as the differential in political capital is high entrepreneurs are likely to be few in number and, at times, to fail. If they do fail then Model 3 -- the service game -- predicts that others will take th eir place; that is the system of exchange has an equilibrium state but has no regard for the successes or failures of particular actors. [12] My intention, of course, is that the prestige-service game bears some resemblance to the dynamics of Big Man exchange systems in parts of highland Papua New Guinea.

So-called Big Man exchange systems take diverse forms (Feil 1987; Godelier and Strathern 1991). Here, I can explore only a few features of those systems and ask whether observed variation can be accommodated to the model I have developed. The contrast between prestige-enhancing exchanges among Mendi and Melpa provides a useful starting point (Lederman 1990). Among the former people many individuals engage in small-scale prestige-enhancing exchanges; that is, as Lederman expressed it, there are many 'little Big Men'. Among the latter people relatively few individuals engage in large-scale prestige-enhancing exchanges and Big Men are 'truly' big; they have more political power, access to more 'wealth' items, probably dispose of more pigs in ceremonial exchanges, and participate within more extensive and sequential ('enchained') exchange networks than Mendi Big Men. These differences correspond to those expected under the prestige-service game where exchanges are financed from, respectively, relatively low and relatively high differentials in political capital. The difference between Mendi and Melpa is thus analogous to that represented by Figures 1b and 1c, respectively. In both cases there is considerable overlap of membership between the service and prestige games; that is, the prestige game is, in part, self-financing.

Further, among both Mendi and Melpa exchanges associated with the prestige game incorporate a principle of escalated (incremental) reciprocation in which more is given than was received and in which it may be only the increment that is taken as the 'measure' of the recipient's indebtedness. Given that in the prestige game actors are rewarded by establishing indebtedness, escalated reciprocation ensures that from time to time the relative prestige accorded two actors vis-[grave{a}]-vis one another is seen to be reversed. This is the outcome of what I have labelled retaliative cooperation-defection (Model 4) and Strathern (1971:11) called 'alternating disequilibrium'. In addition, however, because the game may continue only if debts are eventually paid -- that is, for each actor it is necessary to keep exchange items circulating -- an expectation that more will be received than was given (or, at least, that discounting effects will be ameliorated) may provide a powerful incentive to be patient when dealing wit h a tardy reciprocator. [13]

At least the Melpa system, as depicted by Lederman (ibid.), is one in which relatively few entrepreneurial individuals achieve prestige but, in as much as they are unable to reciprocate those to whom they are indebted or, as necessary, call in debts from those to whom they have extended largesse, these individuals are vulnerable to eventual replacement by others. Ultimately the trust upon which the system is built may be denied to actors with high political capital, and redirected to others, by those with low political capital when the latter experience unacceptably high costs as a result of the continued defection of the former. In turn this suggests that those who play the service game may be, in some sense, the arbiters of success and failure in the prestige game. This would be consistent with Boehm's (1997) argument concerning 'counter-dominant behaviour'. He wrote: 'Morality makes a radically egalitarian outcome possible for humans because morality involves a permanent coalition of an entirely watchful community. Morality and social control are inexorably inter-twined with politics, for the all-powerful moral community defines what is politically legitimate and applies its sanctions accordingly' (ibid.:361). He allowed that despots could arise and that followers might lose control. In the Papua New Guinea highlands, ethnographers have made the same observation in relation, for example, to the Enga where Big Men may fob off those who have financed their prestige-enhancing exchanges 'with promises of future repayment or (less often)' by threatening physical violence (Meggitt 1974:190). Here, of course, political capital is redirected against those who conferred it such that the payoff is a consequence of power rather than of prestige per Se. The prestige-service game is risky for all participants. [14]

To this point I have avoided a crucial issue. Melanesian exchange systems are commonly represented as gift economies (e.g. Gregory 1982; Strathern 1988). Here, items that are exchanged are not alienable from the identity of transactors who, in effect, both exchange and ultimately share parts of each other's identity. As Strathern (1992:177) expressed it, Melanesian gift exchange is 'based on the capacity for actors (agents, subjects) to extract or elicit from others items that then become the object of their relationship' . An extreme interpretation of Strathern's argument would be that in gift exchange no economic value attaches to the items exchanged.

This extreme reading of gift exchange may be accommodated to the models I have developed by simply deleting all payoffs predicated on economic capital (i.e. all E variables in payoff matrices) and asking what consequences this would have for expected outcomes. The outcomes expected from Models lA and 3 would remain unaltered, Model lB would reduce to Model lA and Model 5 would reduce to nonsense. In the last case, barter-trade could be activated only where the exchange implicated social capital and the transaction took the form of Model 2 (see below); although this would seem to approximate Strathern's (1992; see G[ddot{o}]rlich, 1998a) position, neither I nor, perhaps, most other writers are satisfied that considerations of economics can be routinely divorced from barter-trade in Melanesia (e.g. Hughes 1977; Healey 1990).

But, again, this extreme reading of gift exchange would alter Model 2 such that there was no basis other than spite for an actor not to cooperate with an exchange partner and, with repeated transactions and retaliative spite, there would be no relative gain to a non-cooperative actor. The payoff matrix is shown as Table 8 and predicts mutual cooperation as yielding the highest benefit to both actors; the transformed matrix disposes of the paradox of mutual defection inherent in Prisoner's Dilemma. Gift exchange in these circumstances would not be theoretically problematic.

Model 4, the prestige game, would also reduce to nonsense if all considerations of economic capital were deleted from the payoff matrix shown as Table 6. The game, however, could be resurrected in unaltered form if the payoffs shown in Table 6 were translated as 'creditor' (for -[E.sub.1g] [-[E.sub.2g]]) and 'debtor' (for [E.sub.1r] [[E.sub.2r]]) and it was asserted that staying in the game with the perceive status of 'creditor' yielded the highest payoff in terms of prestige. [15]

Despite Strathern's enthusiasm for depicting all or most Melanesian systems of exchange as being free from contamination by economic capital it seems that the empirical ground on which she rests her case is that of forms of exchange made possible by political capital. Under my analyses it is only the prestige game that requires 'the circulation of objects in relations in order to make relations in which objects can circulate' (Strathern 1988:221). Elsewhere she wrote: 'Coercion is essential to the manner in which the "gift" is created. People must compel others to enter into debt: an object in the regard of one actor must be made to become an object in the regard of another. The magic of the gift economy, then, lies in successful persuasion' (1992:177). If gift exchange is thereby reduced to what I have modelled as the prestige game then it is necessary to recognise that this is contingent upon, is serviced by, games that have a quite different logical structure. The alternative would be to collapse the comp lex prestige-service game into unitary form -- gift exchange -- and acknowledge that coercion (underlying the prestige game) and trust (underlying the service game) are two sides of a recursive and overdetermined universe of transactions and transactors. [16]

CODA

The Tierra del Fuegian word mamihlapinatapai and the Dobuan concept of wabuwabu both reveal that human actors may be aware of the formal logic of strategic interactions, of the need to find practical solutions to problems inherent in that logic and of the risks entailed in either the logic itself or in the variety of opportunities presented by that logic. It is in this context that I turn briefly to the emergence of card-playing in the Papua New Guinea highlands for it is my understanding that, in part, this is analogous to the notion of 'setting a thief to catch a thief' or, with a nod to Melanesia and a post-contact Kubo innovation, 'setting a sorcerer to catch a sorcerer'. I refer, particularly, to situations in which people gamble for money by playing card games in which chance, and not strategy, is the primary determinant of outcomes (Maclean 1984; Zimmer 1986, 1987).

In Papua New Guinea gambling with cards emerged in contexts where some individuals had access to sources of wealth that were extrinsic to existing or conventionally-accepted networks of social relations. Those individuals acquired the where-with-all for playing the prestige game freed from the constraint of trusting relationships with others who, in customary arrangements, had serviced and, ultimately, acted as guarantors to the prestige game. But the Gende and Maring cases as reported by Zimmer (1986) and Maclean (1984), respectively, differed in scale.

Among the Gende, participants in card games were people, both male and female, who would have usually interacted in the service game and not people who would have usually interacted in the prestige game and the outcome was the redistribution of sums of money that entered the community from outside (e.g. when men returned after periods of employment elsewhere). The amounts of money were, however, relatively low. Among the Maring, more money was available to more people and much of this was generated through local cash cropping. Here it was men who gambled with cards, the stakes were higher and the network of participants reached beyond local communities; the ultimate outcome was to redistribute much of the money that would otherwise have tended to flow towards the owners of small trade stores. In both cases card playing served to redistribute unpredictable or communally-unregulated sources of unequal wealth. And, in both cases, gambling with cards is understandable from the perspective of game theory.

Colman (1995:23-32) discussed the intractable nature of games of chance in which uncertainty prevails and, in a different context, referred to circumstances in which game theory predicts that rational actors will randomize decisions (ibid.:62-9; see also Miller 1997). Gambling with cards, where outcomes are grounded in chance, should not be seen as similar to any of the exchange situations represented by Models 2 to 5 of this article for the simple reason that it does not entail strategic decisions (cf. Zimmer 1986. Here, I follow Colman in distinguishing 'risk' and 'uncertainty'; in situations of the latter kind it is not possible to assign probabilities to possible outcomes and, hence, not possible to reach strategic decisions). Rather, it may be understood as a means whereby people regained control over the unregulated bestowal of political capital by recourse to a randomization strategy that had the potential to recreate a seemingly level playing field. This interpretation is similar to Miller's (1997:32 7) suggestion, based in considerations of game theory, that 'Britain's adoption of a national lottery could be construed as a convenient way of promoting national unity and an illusion of fairness in the face of apparently indestructible class divisions and economic collapse'. Nor, however, from the perspective of game theory, should it be surprising that the role of card playing might decline or take other forms as a greater proportion of people gained access to extrinsic sources of wealth or that a subset of individuals -- for example, young men among the Gende of Madang Province -- should turn to a potentially dangerous and strategic card game that provided opportunities for some of those individuals to accrue political capital (Sexton 1987; Zimmer 1987).

ACKNOWLEDGMENTS

I thank Joachim G[ddot{o}]rlich, whose own article in Oceania provided the stimulus for mine. Thanks also to Steven Gaulin, Monica Minnegal, Neil Maclean, Thomas Reuter and anonymous referees for their comments on earlier drafts. Support from the Australian Research Council, and the hospitality of the Anthropology Programme and the Department of History and Philosophy of Science at The University of Melbourne, facilitated completion of this work.

NOTES

(1.) In biological approaches to game theory the notion of an evolutionarily stable strategy (ESS) is used with reference to variants or combinations of variants that, in fact or in theory, are unbeatable within the established context of a game (Maynard Smith 1974, 1982). Game theoretical models are, however, used in two ways by biologists. On the one hand, they expose existing variants to imaginary variants to contribute to an understanding of why the status quo prevails and, on the other hand, ask what evolutionary consequences would follow if existing variants are exposed to alternative contexts or competing new variants (e.g. Broom et al. 1997). In both eases unbeatable variants or combinations are diagnosed as ESSs. The question addressed in the first case is, however, ecological; it is concerned with the reproduction or maintenance of form. Here, to avoid a connotation of evolution, I prefer to translate ESS as 'ecologically secure solution'.

(2.) A promising recent development from game theory, known as drama theory, is based on the 'idea that games are not static, one shot deals decided by rationality, but dynamic situations that can be utterly transformed by the emotions of the players' (Matthews 1998:29; see also Howard 1994, Bryant 1997). Drama theory accommodates the fact that actors may transform the game in the course of an engagement, that the 'rules of play' are contingent upon circumstances of the moment. The present article recognises that particular outcomes may establish possibilities for different patterns of exchange relationships -- indeed, Models 3 and 4 must be understood in these terms - but does not achieve the intent of drama theory and identify sequential transformations that may arise within the course of a single interaction.

(3.) Colman (1995:111-2) described Chicken as 'the prototype of the dangerous game'. He described the most familiar version as follows:

Two motorists speed towards each other. Each has the option of swerving to avoid a head-on collision and thereby being 'chicken' or of resolutely driving straight ahead. If both players are 'chicken', the outcome is a draw [ldots] and if both drive straight ahead, they risk death or serious injury. But if one chickens out by swerving, while the other exploits this cautious choice by driving straight on, the 'chicken' loses face (but is not killed) and the 'exploiter' wins a prestige victory based on courage or machismo (ibid., paraphrased).

Colman and Wilson (1997:27) noted that encounters with the logical structure of Chicken occur 'frequently in everyday strategic interactions involving risk talking' and in situations in which an actor 'gains advantage from deliberately appearing irrational'.

(4.) The choice of labels for different categories of 'capital' is fraught with hazard (e.g. Milner 1994:8-11). My choice of economic, social and political converges upon Sahlins' (1974:200) division into economic, moral and social and Zimmer's (1986:258) division into credit, respect and prestige. Bourdieu (1990) wrote of four varieties of capital -- economic, social, cultural and symbolic -- while others have recognised two types and, for example, separated material from symbolic, material/economic from socin-political or economic/political from social (e.g. Knauft 1996:106).

(5.) G[ddot{o}rlich] (1998b:310) considered that, to varying degrees, exchange entails a problem of 'coordination' in which it is necessary that actors determine 'the exchange rates or at least the range inside which the exchange rates oscillate'. In this article, by defining items as being of equivalent or non-equivalent economic value from the perspective of each actor exchange may be modelled without reference to either variation across societies with respect to empirical issues of object value, quantity and calculation or anthropological debate concerning these issues (e.g. Gell 1992b; Strathern 1992). For example, if two actors routinely exchange items that differ with respect to labour input, the mere fact that they are willing to sustain the exchange is taken to imply that the seemingly disadvantaged actor has accommodated other material factors (e.g. supply, security, necessity) into his or her accounting. The 'coordination problem', in G[ddot{o}]rlich's sense, is undoubtedly important but it is assum ed here that actors have resolved this problem to theft own satisfaction before engaging in an exchange transaction.

(6.) Risk (and, hence, the potential for conflict) arises from a variety of sources each of which could be treated as a separate variable. In this article these are collapsed as a single cost variable arising from the 'impact of risk'. This simplifies presentation and interpretation of the models.

(7.) Among Kubo, of the interior lowlands of Papua New Guinea, the exchange of young women as wives is ideally, and sometimes actually, immediate and the exchange and dispatch of pigs is often immediate. On one occasion among Kubo, after protracted discussion and negotiation, a brother and sister, exchanged K20 notes, in public and simultaneously, by way of intermediaries who carried the money from one party to the other. The exchange sought to restore social capital that had been eroded by the dispute. Sahlins (1974:194) referred to other ethnographic cases of literally immediate exchange.

(8.) The necessary conditions for reciprocal altruism are that donors on one occasion are recipients on another, that the number of opportunities to 'play' is multiple and indefinite, that capacities for individual recognition and for punishing defectors exist, and that the benefit to a recipient during a single act of exchange is greater than the cost to a donor (Dwyer and Minnegal 1997:94, Wilkinson 1984). Rules other than tit-for-tat and alternative contexts that may facilitate stable cooperative outcomes in games of Prisoner's Dilemma have been proposed by Nowak and Sigmund (1992, 1993), Frean (1996) and Roberts and Sherratt (1998).

(9.) Where the exchange of equivalent items is delayed, discounting effects may arise and economic values may be asymmetrical and biased in favour of actors who were tardy in reciprocating intended exchanges. This, of course, would increase risk and potentially increase costs to other actors. It would also have the logical consequence that the economic capital associated with the items in question was not, in fact, identical. This complication is not considered any further.

(10.) G[ddot{o}]rlich's (1998b) game theoretical analysis of ceremonial exchange differs greatly from mine. He represents this mode of exchange in terms of a cooperation problem (analysed as a Prisoner's Dilemma) with an embedded bargaining component that facilitates the negotiation of prestige. However, in the absence of models that are mathematically grounded his argument is difficult to follow because it does not show how the continual cancellation of debt with payoffs biased in favour of recipients, as predicted under a repeated Prisoner's Dilemma, may coexist with the continual creation of debt with payoffs biased in favour of donors, as required for the establishment of prestige. Nor is it clear why bargaining, as discussed by G[ddot{o}]rlich, should not routinely favour one actor in each dyadic exchange relationship; to this extent his model appears to conflict with ethnographic reality. Further, G[ddot{o}]rlich does not allow for the fact that ceremonial exchange is contingent upon the existence of mu ltiple partners each of whom depends upon an established servicing network (Model 3 of this article). A major limitation of his analyses arises from the failure to present matrices that depict different varieties of payoff in algebraic form.

(11.) Fortune (1963:234) wrote of the 'pride' associated with Kula exchange: 'This pride, however, is not as the pride of the potlatch giver. Far from it. It is based on great having, not on generous giving. All giving is for equal return, and all fallen pride and shame is for loss of equal return'. The distinction here is that implicit in the logical form of the sharing and prestige games.

(12.) Colman and Wilson (1997) argued that the persistence of a low but stable proportion of individuals with Antisocial Personality Disorder (APD) within western societies may be modelled as a game of Chicken. Their article was a response to an earlier reading of APD in terms of Prisoner's Dilemma (see Mealey 1995) and the nature of their response is thus analogous to my reexamination of the argument offered by F[ddot{o}rlich (1998a,b). The general problem here is that Prisoner's Dilemma has tended to be prioritized as a model for exploring strategic interactions. Ridley's (1997) The Origins of Virtue provides the extreme case but, in a similar way, the evolutionary psychologists Cosmides and Tooby (1992) appear to equate all social exchange with reciprocal altruism and, thereby, prioritize Prisoner's Dilemma as an analytical tool.

(13.) Some writers have drawn attention to the importance of home production as a means of financing political capital (e.g. Strathern 1978; Lederman 1990). This does not jeopardize my interpretations. It means only that the servicing network is tightly constrained by kinship but does not negate the moral responsibilities of a would-be entrepreneur to reciprocate those kin. Indeed, even in the extreme case that a would-be entrepreneur was self-financing by, for example, increased effort and production, he or she would have reduced commitment in other endeavours relative to local conventions and, hence, be indebted to a network of other actors who were inconvenienced by that abnegation of responsibilities.

(14.) In the final analysis I have argued that it is only in the service component of the prestige-service game that logical and practical logical are likely to be congruent. This may be of more than theoretical interest. Under the models I have developed, access to the prestige game is possible only via an apprenticeship of cooperative service that is structured in accordance with the game of Chicken (Gregory 1982:52-3).

(15.) A less extreme approach to gift exchange might be achieved by weighting different types of capital such that the importance of economic capital was reduced (but not cancelled) relative to social or political capital. In fact, this matter was considered by Barth (1959:18) who discussed the problem of incorporating incommensurate variables into an analysis and allowed that 'persons will at times renounce material gains in favour of intangible gains of "status" and "esteem"'; his own analysis required that in some circumstances actors placed less weight on economic than on socio-political considerations. Analyses that adopted this more moderate position would leave space for economic factors within gift exchange and, in line with G[ddot{o}]rlich's (1998a,b) understanding and a central thesis of the present article, recognise that barter-trade and gift exchange represent different permutations of the same underlying variables.

(16.) In parts of Papua New Guinea the prestige game is, at least in part, financed by barter-trade (e.g. Healey 1990) which, like the intraregional service game, has the logical form of Chicken. Thus, while my analysis of exchange systems resonates with that of Gell (1992b), I differ most strongly in identifying strong structural similarities between the barter-trade and service games on the one hand and weaker similarities between the sharing and prestige games on the other. Under Gell's argument sharing and service on the one hand and prestige and barter-trade on the other were regarded as structurally -- indeed, evolutionarily -- connected.

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A generalized payoff matrix for an exchange interaction between two actors. E, S, P and --R refer, respectively, to economic capital, social capital, political capital and the impact of risk. The subscripts 1 and 2 identify the relevant actor, the subscripts r and g refer to items that are, respectively, received and given by the nominated actor, [E.sub.1] = [[E.sub.1r] -- [E.sub.1g]] and [E.sub.2] = [[E.sub.2r] -- [E.sub.2g]]. Payoffs to Actor 1 are unbracketed, those to Actor 2 are bracketed.

 Actor 2
 cooperate
Actor 1 cooperate [E.sub.1] + S [[E.sub.2] + S]
 defect [E.sub.1r] + S + [P.sub.1] [-[E.sub.2g]]
 defect
Actor 1 cooperate -[E.sub.1g] [[E.sub.2r] + S + [P.sub.2]]
 defect -[R.sub.1] [-[R.sub.2]]

A payoff matrix for an intraregional, immediate exchange. Codes have the meanings assigned in Table 1. A dash indicates 'not applicable'.

 Actor 2
 cooperate defect
Actor 1 cooperate [E.sub.1] + S [[E.sub.2] + S] --
 defect -- 0 [0]

A payoff matrix for an intraregional, delayed exchange in which political capital is not relevant. Codes have the meanings assigned in Table 1. Actual payoffs are shown on the left; ranked payoffs are shown on the right. A formal representation of this payoff matrix would show t (temptation), r (reward), p (punishment) and s (sucker) in the locations where I have recorded the ranks 4 to 1, respectively. The structure of the matrix conforms to Prisoner's Dilemma if t[greater than] r[greater than] p[greater than]s and 2r[greater than] t + s; where t[greater than]r[greater than]s[greater than]p the game is Chicken.

 Actual payoffs
 Actor 2
 cooperate defect
Actor 1 cooperate S[S] [-E.sub.1g][[E.sub.2r]+ S]
 defect [E.sub.1r]+S[[-E.sub.2g]] 0[0]
 Ranked payoffs
 Actor 2
 cooperate defect
Actor 1 3[3] 1[4]
 4[1] 2[2]

A disaggregated payoff matrix for an intraregional, delayed exchange in which political capital is not relevant (cf. Table 3). Codes have the meanings assigned in Table 1. The matrix shows that a cooperative move by one actor yields payoffs of -[E.sub.1g] to that actor and [E.sub.1r] + S to the other actor; thus, if both actors cooperate each receives S (i.e. [E.sub.1r] - [E.sub.1g] = 0) as shown in the conventional payoff matrix. Other values in the conventional matrix may be assembled from the disaggregated matrix in similar ways.

 own payoff other's payoff
Actor cooperate -[E.sub.1g] [E.sub.1r] + S
 defect 0 0

A payoff matrix for an intraregional, delayed exchange in which political capital is relevant. Codes have the meanings assigned in Table 1. See text for further explanation.

 Actor 2
 cooperate
Actor 1 cooperate S[S]
 defect [E.sub.1r] + S + [P.sub.1] [[-E.sub.2g]]
 defect
Actor 1 cooperate [-E.sub.1g][[E.sub.2r] + S + [P.sub.2]]
 defect [-R.sub.1][[-R.sub.2]]

A payoff matrix for the activation of political capital. Codes have the meanings assigned in Table 1 with the exception that '-[R.sub.1]' and '-[R.sub.2]' represent exclusion from the game. Actual payoffs are shown on the left; ranked payoffs are shown on the right. See text for further explanation.

 Actual payoffs
 Actor 2
 cooperate defect
Actor 1 cooperate 0 [0] [-E.sub.1g] [[E.sub.2r]]
 defect [E.sub.1r] [-[E.sub.2g]] `[-R.sub.1]' [`[-R.sub.2]']
 Ranked payoffs
 Actor 2
 cooperate defect
Actor 1 3 [3] 4 [2]
 2 [4] 1 [1]

A payoff matrix for an interregional exchange. Codes have the meanings assigned in Table 1. Payoffs to Actor 1 are assigned ranks for the circumstance in which - [R.sub.1] [less than] - [E.sub.1g].

 Actor 2: on home territory
 cooperate
Actor 1: cooperate [E.sub.1] [[E.sub.2]]
off home territory rank 3
 defect [E.sub.1r] [[-E.sub.2g]]
 rank 4
 defect
Actor 1: cooperate [-E.sub.1g] [[E.sub.2r]]
off home territory rank 2
 defect [-R.sub.1] [[-R.sub.2]]
 rank 1

A payoff matrix for an intraregional, delayed exchange in which economic capital and political capital are not relevant (cf. Table 3). Codes have the meanings assigned in Table 1. Actual payoffs are shown on the left; ranked payoffs are shown on the right. Under this matrix the ranks of payoffs to an actor from mutual cooperation, retaliative cooperation--defection and mutual defection are 3.5, 2.5 [i.e. (3.5 + 1.5)/2] and 1.5.

 Actual payoffs Ranked payoffs
 Actor 2 Actor 2
 cooperate defect cooperate defect
Actor 1 cooperate S [S] 0 [S] 3.5 [3.5] 1.5 [3.5]
 defect S [0] 0 [0] 3.5 [1.5] 1.5 [1.5]