Behavioral foundations of reciprocity: experimental economics and evolutionary psychology.

Hoffman, Elizabeth ; McCabe, Kevin A. ; Smith, Vernon L. 等

I. INTRODUCTION

Theorists have long studied the fundamental problem that cooperative, socially efficient outcomes generally cannot be supported as equilibria in finite games. The puzzle is the occurrence of cooperative behavior in the absence of immediate incentives to cooperate. For example, in two-person bargaining experiments, where noncooperative behavior does not result in efficient outcomes, we observe more cooperative behavior and greater efficiency than such environments are expected to produce. Similarly, in public good experiments with groups varying in size from four to 100 people, the participants tend to achieve much higher payoff levels than predicted by noncooperative theory. Moreover, examples of cooperative behavior achieved by decentralized means have a long history in the human experience. Anthropological and archaeological evidence suggest that sharing behavior is ubiquitous in tribal cultures that lack markets, monetary systems, or other means of storing and redistributing wealth (see, e.g., Cosmides and Tooby [1987; 1989]; Isaac [1978]; Kaplin and Hill [1985]; Tooby and De Vote [1987]; Trivers [1971]).

In this paper we draw together theoretical and experimental evidence from game theory, evolutionary psychology, and experimental economics to develop a reciprocity framework for understanding the persistence of cooperative outcomes in the face of contrary individual incentives. The theory of repeated games with discounting or infinite time horizons allows for cooperative solutions, but does not yield conditions for predicting them (Fudenberg and Tirole [1993]). Recent research in evolutionary psychology (Cosmides and Tooby [1987; 1989; 1992]) suggests that humans may be evolutionarily predisposed to engage in social exchange using mental algorithms that identify and punish cheaters. Finally, a considerable body of research in experimental economics now identifies a number of environmental and institutional factors that promote cooperation even in the face of contrary individual incentives (Davis and Holt [1993]; Isaac and Walker [1988a,b; 1991]; Isaac, Walker and Thomas [1984]; Isaac, Walker and Williams [1991]). Moreover, these experimental results indicate that trust and trustworthiness play a much greater role than the evolutionary psychologists' punish-cheaters model would suggest. We hypothesize that humans' abilities to read one anothers' minds (Baron-Cohen [1995]) in social situations facilitates reciprocity.

II. REPEATED GAMES

Repeated-game theory offers two explanations of cooperation based on self-interest: self-enforcing equilibria and reputations. Self-enforcing equilibria are based on the idea that players can credibly punish noncooperative defections. The nagging problem with self-enforcing cooperative equilibria is that there are many equilibria in such games with cooperation being only one possibility.

Experiments demonstrating that subjects cooperate in games with repeated play and relatively short finite horizons (Selten and Stoecker [1986]; Rapoport [1987]) suggest reputations are important in games with incomplete information (Kreps et al. [1982]). The idea is that if players are uncertain about other players' types, then the possibility emerges that players will mimic (develop a reputation as) a type different from their own. In circumstances where cooperation is mutually beneficial players have an incentive to mimic cooperative behavior.

In the examples given by Kreps et al. [1982], players rationally compute strategies based on (utility or payoff) type uncertainty. They cooperate from the beginning until near the end of the game, and then defect. This is not, however, the pattern observed in experiments, where it is common for cooperation to develop out of repeated interactions; also, defection near the end is often not observed.

The strength of the theory is that it is based on individual (but longer run) self-interest, and is parsimonious. Its weakness is that it admits many possible equilibria without suggesting why cooperation is the most likely outcome. Moreover, for reputation-based equilibria, people must entertain beliefs about certain types of people.

But where do these beliefs come from? We introduce the hypothesis that types emerge from the evolutionary fitness of certain cognitive abilities which predispose many people towards reciprocity. Actual circumstances and experiences may lead to reciprocal behavior by many persons. Not everyone has to be a particular type; variability is the stuff from which selection occurs and which allows nature to adapt to change. But the type must exist in sufficient numbers for people to believe that reciprocity pays. And if reciprocity pays, culture and norms develop to specify the forms that reciprocity will take.

III. MENTAL ALGORITHMS FOR SOCIAL EXCHANGE: STRATEGIES IN HUMAN COGNITION THAT SUPPORT COOPERATION

The complex organization of the human mind is thought to be the product of at least a few million years of evolutionary adaptation to solve the problems of hunting and gathering.(1) Evolutionary psychologists hypothesize that these problems were solved not only by neurobiological adaptations, but also by adaptations in human social cognition (see Cosmides and Tooby [1992], hereafter CT, and the references therein). The idea is that humans have special and highly developed cognitive mechanisms for dealing with social exchange problems: that is, mental modules for solving social problems are as much a part of the adapted mind as our vision and hearing-balance faculties.(2)

Examples of mental "computational" modules that solve specialized design problems include vision, language and "mind reading." The mechanism which constitutes vision involves neural circuits whose design solves the problem of scene analysis (Marr [1982]). The solution to this problem employs specialized computational machinery for detecting shape, edges, motion, bugs (in frogs), hawks (in rabbits), faces, etc. Just as we learn by exposure to see and interpret scenes without being taught, we learn to speak without formal training of any kind.

Although culture is known to operate on our mental circuitry for language learning, the deep structure of language is common across cultures (Pinker [1994]). Normal English-speaking preschoolers can apply mental algorithms to root words to form regular noun plurals by adding "s" and the past tense of regular verbs by adding "ed" (Pinker [1994, 42-43]). The preschooler even "knows" that you can say that a house is mice-infested but never that it is rats-infested, that there can be teethmarks but never clawsmarks - the mental algorithm here allows compound words to be formed out of irregular plurals but never out of regular plurals. This is because of the way the unconscious brain works: regular plurals are not stem words stored in the mental inventory, but words derived algorithmically by the inflectional rule to add "s." Preschoolers in all languages automatically make these kinds of distinctions without being taught by their mothers or their teachers (Pinker [1994, 146-47]).

That the mind contains blueprints for grammatical rules is further indicated by a language disorder in families which appears to be inherited like a pedigree with a dominant gene. English speakers afflicted with this disorder are unable to inflect root words to form derivatives such as the "s" rule for obtaining plurals.

"Mind reading" - the process of inferring the mental states of others from their words and actions - facilitates "social understanding, behavioral predictions, social interaction, and communication" (Baron-Cohen [1995, 30]). Autism in children makes them mind blind - they are not automatically aware of mental phenomena in others, and cannot "mind read".(3) A genetic basis is suggested by its greater risk in identical twins and biologically related siblings. Baron-Cohen [1995, 88-95] implicates the amygdala and related areas of the brain as jointly controlling the ability to detect eye direction in others and to interpret mental states (have a theory of mind) in others. Other detector mechanisms appear to include "friend or foe" - cooperation is not automatic for foes - and the "fight or flight" response to sudden danger.

The hypothesis that our minds are also predisposed to learn behavioral responses that promote cooperative outcomes does not mean that we are born with such behavioral responses. We only need to be born with the capacity to learn such responses developmentally from social exposure, much as we are born with the capacity to learn any language but not with the ability to speak any particular one. A capacity for the natural learning of strategies that induce cooperation in social exchange has fitness value. But the implementational form of what is learned varies widely, depending upon the environment, accidents of nature, and how parental, familial, and societal units organize exchange processes. Consequently, "culture" is endlessly variable, but, functionally, reciprocity is universal.

Naturally selected fitness strategies are hypothesized to be embodied in the designs that modulate reasoning about social exchange. An analysis of these strategies allows one to deduce the behavioral characteristics of the associated mental algorithms. This analysis also allows predictions about human responses in reasoning experiments of the kind that we summarize below. These psychology experiments are of particular interest to experimental economists because they complement subject behavior in many games of strategic interaction.

Consider the standard two-person Prisoner's Dilemma (PD) game, but think of the entries corresponding to C (cooperate) or D (defect) for the row and column players as net benefits and net costs measured in units that increase (or decrease) the individual's inclusive fitness. C might represent the strategy "trade," while D might represent "steal." As discussed above, game theory predicts that mutual cooperation will not emerge in a single-move game - people are all self-interested "foes."

Imagine a tournament that matches pairs from a large population of organisms so that the same two individuals are never matched a second time. Each member is matched, reproduces itself, and dies. The offspring inherits the strategy choice propensity of the parent, and the number of offspring is proportional to the payoff gains of the parent in its matched plays of the game. Each generation repeats this process.

Repeated-game principles can be used to analyze equilibrium outcomes in such a game. Repeat interaction is a prominent characteristic of social exchange. Needs are rarely simultaneous. But, long before human societies invented a generally accepted medium of exchange, various cultural mechanisms provided social adaptations which allowed delayed mutual benefits to be gained: I share my meat with you when I am lucky at the hunt, and you share yours with me when you are lucky. Although this is commonly referred to as reciprocal altruism, we prefer to call it reciprocity. I am not altruistic if my action is based on my expectation of your reciprocation.

Reciprocity leads naturally to property rights. If I grow corn and you grow pigs, and we exchange our surpluses, then we each have an interest in the other's property right in what is grown. If either of us plays "steal," that ends the trading relationship. Hence, mutual recognition and defense of informal property right systems need not require the pre-existence of a Leviathan.

But how might such mutual cooperation emerge in a repeated PD game? We know from the work of Axelrod and Hamilton [1981] that strategy C cannot be selected for in repeated play, but that the contingent cooperative strategy, T (tit-for-tat), can be selected for. In general any strategy, including T, can successfully invade a population of defectors if (and only if) it cooperates with cooperators and punishes defectors (Axelrod [1984]). As noted by CT [1992, 176-77], it is an empirical issue to determine which strategy, out of this admissible set, is actually embodied in human cognitive programs.

The need to solve the PD problem to achieve cooperation provides an abstract schema for organizing our thoughts about cooperation beyond immediate kin. However, simply referring to the motivating example of the PD will not carry us to a full understanding of human social exchange. In particular, it will not help us understand cooperative behavior toward anonymous strangers when there is no prospect for punishment. This is an anomaly in the CT evolutionary paradigm.

An important question for the evolutionary paradigm is whether the mental algorithms for social exchange consist of a few content-free generalized rules of reasoning, or whether they consist of designs specialized for solving social exchange problems. Economic/game theory is driven by the principle that humans naturally use content-free generalized rules of reasoning in solving decision problems. If this is so, why is economics so hard to teach? If these rules come only from culture, where does culture come from?

CT [1992] argue that the evolutionary perspective favors specialized over generalized rules. General rules, applicable to any subject matter, "will not allow one to detect cheaters ... because what counts as cheating does not map onto the definition of violation imposed by the propositional calculus. Suppose we agree to the following exchange: 'If you give me your watch then I'll give you $20.' You would have violated our agreement - you would have cheated me - if you had taken my $20 but not given me your watch. But according to the rules of inference of the propositional calculus, the only way this rule can be violated is by your giving me your watch but my not giving you $20" (CT [1992, 179-80]). That is, the way you falsify "if P, then Q," statements is to look for "P, not Q," evidence. In this example, giving me your watch is the P statement; my not giving you $20 is the not-Q statement. If such rules were the only ones contained in our minds, we would have no special ability to detect cheating.(4)

One theme in the CT research program is to design experiments that will test these kinds of propositions (CT [1992, 181-206]). The selection task that CT employ was developed by Wason [1966], whose motivation was to inquire as to whether the ordinary learning experiences of people reflected the Popperian hypothesis-testing logic outlined above. The procedure uses four cards, each carrying one of the labels, P not-P, Q, not-Q on the side facing up, and another of the same four labels on the side facing down. Each card corresponds to some situation with one of the labeled properties. The rule is violated only by a card that has a P on one side and a not-Q on the reverse side.

Subjects are asked to indicate only the card(s) that definitely need to be turned over in order to see if any cases violate the rule. The correct answer is to indicate the cards showing P (to see if there is a not-Q on the other side) and not-Q (to see if there is a P on the other side). In one example, a secretary's task is to check student documents to see if they satisfy the rule: If a person has a "D" rating, then his document must be marked code "3." Four cards show D, F, 3, and 7, and subjects should indicate the cards showing the letter D and the numeral 7. Less than 25% of college students choose both of these cards correctly.

Now consider a law which states that "If a person is drinking beer, then he must be over 20 years old." Out of four cards which also include "not drinking beer" and "25 years old" the correct response is to choose the card "drinking beer" and the card "16 years old." In this experiment about 75% of college students get it right. Why the difference from the previous example?

Although people do better in more familiar examples such as: "Ira person goes to Boston, then he takes the subway," less than half get it right. A survey of this literature (Cosmides [1989]) suggests that "Robust and replicable content effects were found only for rules that related terms that are recognizable as benefits and cost/requirements in the format of a standard social contract" (CT [1992, 183]). Sixteen out of 16 experiments using social contracts showed large content effects. Fourteen out of 19 experiments which did not use contract rules produced no content effect, two produced a weak effect, and three produced a substantial effect.

These findings launched a number of studies designed to separate the social contract hypothesis from confounding interpretations, such as familiarity, or that the social context merely facilitates Popperian reasoning. CT report that the alternative hypotheses have not survived experiments designed to separate them from the cheater-detection hypothesis.(5)

IV. OBSERVABILITY, COMMUNICATION, AND INTENTIONALITY SIGNALING

If humans are preprogrammed to learn to achieve cooperative outcomes in social exchange, then factors that facilitate the operation of these natural mechanisms should increase cooperation even in the presence of contrary individual incentives. For example, cooperation should increase if individuals can observe and monitor one anothers' behaviors, even if there are no direct mechanisms for enforcing specific behaviors. In Baron-Cohen's [1995] model of mind reading, the eye direction, shared attention, and intentionality detectors are used to identify and ratify the volitional states of others. Observation and monitoring activate one or more of these detectors. Moreover, if it is possible for agents to directly punish cheating by other agents, cooperation should increase even further.

Similarly, if agents can communicate with one another, they can frame a group decision as a social exchange problem and ratify one anothers' volitional states, thus activating natural inclinations to cooperate for increased individual gain. Thus, communication can increase cooperation even if there are no effective mechanisms for monitoring and punishing cheaters.

Voluntary Contribution Experiments

The standard environment for studying the free rider problem in the allocation of public goods is the voluntary contribution mechanism (VCM), extensively studied by Isaac and Walker, and their coauthors (Isaac, McCue and Plott [1985]; Isaac, Schmitz and Walker [1989]; Isaac and Walker [1988a,b]; Isaac, Walker and Thomas [1984]; Isaac, Walker and Williams [1991]). In a VCM experiment, each subject is given a set of tokens at the beginning of each period. The subject may invest tokens in an individual exchange, with a fixed monetary return per token, and/or a group exchange, which returns money to the subject as a function of the total contributions of all the subjects in the experiment.

Typically the individual incentives are designed to make strong free riding, or zero contributions to the group exchange, the dominant strategy for each subject. On the other hand, the highest joint payoff for all subjects is achieved when all subjects contribute 100% of their tokens to the group exchange.

Isaac and Walker and their coauthors, as cited above, find that contributions to the group exchange are sensitive to differences in the rules of message exchange that relate to our previous discussion of cognitive mechanisms for social exchange. With subject groups of four or ten subjects, if subjects make contributions in private, if there is no identified target level of contributions, and if they do not communicate with one another at any time during the experiment, then contributions to the group exchange decline from about 40% of tokens in period one to about 10% of tokens in period 10 (Isaac and Walker [1988a]; Isaac, Walker and Thomas [1984]). These results extend to large groups of 40 or 100 people, but per capita contributions actually increase relative to groups of size four or ten in some treatments.

In the same experimental environment, however, if subjects can talk with one another for a short period before each decision, contributions to the group exchange quickly rise to almost 100% of tokens, even if actual investment decisions are made in private (Isaac and Walker [1988b]). These results illustrate the importance of "cheap talk" communication in creating an environment in which agents expect one another to behave cooperatively and they abide by the reinforced norm even when all decisions are made in private and no individual's defection can be detected by others.

The results can also be interpreted in a signaling context. During the communication phase, individuals verbally signal that they will behave cooperatively and that they expect others to reciprocate. During the decisionmaking phase, individuals generally abide by the norm reinforced by the signal, and a cooperative outcome is achieved. While no direct punishment can be inflicted by other subjects in the event of defection, other subjects can exact general punishment by defection against other subjects in future rounds.

In other experiments (Isaac, Schmitz and Walker [1989]), the experimenter establishes a minimum provision-point contribution to the group investment. Comparing results with and without a provision point, and allowing no communication, contributions to the group account increase with the provision point. When the provision point is 100% of tokens, contributions rise even further, although many groups fail to attain it.

From a signaling perspective, the provision point signals an expected joint level of contribution to the group account, and helps to induce common expectations of substantial contributions to the group account. With equal endowments the implied signal is that each subject should contribute (1/n)th of the announced provision point.

Ultimatum and Dictator Experiments

Ultimatum and dictator experiments illustrate the importance of observability, shared expectations of social norms, punishment, and signaling in enforcing reciprocity behavior. In an ultimatum game, player 1 makes an offer to player 2 of $X from a total of $M. If player 2 accepts the offer, then player 1 is paid $(M - X) and player 2 receives $X; if player 2 rejects the offer, each gets $0. In the dictator game, player 2 must accept player 1's offer.

Under the usual rationality assumptions the noncooperative equilibrium of the ultimatum game is for player I to offer player 2 the smallest dollar unit of account, and for player 2 to accept the offer. In the dictator game player 1 offers player 2 nothing. In the ultimatum game, however, player 2 can punish player 1 for "cheating" on an implied social norm of reciprocal sharing across time, in social exchange, by rejecting player 1's offer. That response is a dominated strategy, if viewed in isolation, since both players would be financially better off even with a vanishingly small offer. But, in the absence of common knowledge of self-interested behavior, the possibility of punishment may change player 1's equilibrium strategy.

In Kahneman, Knetsch and Thaler [1986] (hereinafter KKT), players 1 and 2 in an ultimatum game are "provisionally allocated" $10 and player 1 is asked to make an initial offer to "divide" the $10 between the two players. Player 2 may veto the division, in which case they both get $0. Kahneman and his coauthors find that most often player 1 offers $5 to player 2; offers of less than $5 are sometimes rejected. Although there are some differences, the general features of these results have been replicated in cross-cultural comparisons suggesting that the results are not strongly culture-specific (Roth, Prasnikar, Okuno-Fujimara and Zamir [1991]). This suggests that the explanation may transcend culture.

Forsythe, Horowtiz, Savin and Sefton [1994] (hereinafter FHSS) replicate KKT's results from the ultimatum game, and also study the dictator game. They find that about 20% of dictator player 1s offer nothing to their player 2 counterparts, as noncooperative game theory would predict; however, it is more common for player 1 to offer $5 than to offer nothing, and offers of $1, $2, $3, and $4 are approximately evenly distributed. Thus, removing the threat of punishment reduces sharing behavior, but not by as much as game theory predicts.

Recognizing that the prospect of punishment might create expectations that change player 1's behavior, Hoffman, McCabe, Shachat and Smith [1994] (hereafter HMSS) consider experimental treatments explicitly designed to affect subject expectations about operating norms of social exchange. The experimental instructions that describe the different treatments might be viewed as signals to the subjects of the expected social norm operating in each experiment.

Brewer and Crano [1994], a recent social psychology textbook, lists three norms of social exchange that may apply in ultimatum games. From our perspective, norms are the product of culture interacting with mental modules in order to solve specific problems of social exchange. Such norms can then inform a theory of mind mechanism as to another's volitional state. Equality implies that gains should be shared equally in the absence of any objective differences between individuals suggesting another sharing rule. Equity implies that individuals who contribute more to a social exchange should gain a larger share of the returns. Reciprocity implies that if one individual offers a share to another individual, the second individual is expected to reciprocate within a reasonable time. We distinguish negative reciprocity - the use of punishment strategies to retaliate against behavior that is deemed inappropriate - and positive reciprocity - the use of strategies that initiate or reward appropriate behavior.

The designs of KKT and FHSS invoke the equality norm. No distinction is made between the two individuals "provisionally allocated" $10, and they are told to "divide" the money. Hence, deviations from equal division are more likely to be punished as "cheating" on the social exchange. Using the same task description, HMSS replicate the FHSS results in a "random/divide $10" treatment.

To invoke equity, HMSS explore two variations on their random/divide $10 treatment in a 2x2 experimental design. First (the exchange treatment), without changing the reduced form of the game, HMSS describe it as a market in which the "seller" (player 1) chooses a price (division of $10) and the "buyer" (player 2) indicates whether he or she will buy or not buy (accept or not accept). From the perspective of social exchange, a seller might equitably earn a higher return than a buyer. Second (the contest treatment), they make each seller earn the property right to be a seller by scoring higher on a general knowledge quiz than buyers. Winners are then told they have "earned the right" to be sellers. Going back to Homans [1967], equity theory predicts that individuals who have earned the right to a higher return will be socially justified in receiving that higher return.

Figure 1 reproduces HMSS's random/divide and contest/exchange experimental results. Social exchange theory predicts that, in a situation in which it is equitable for player 1 to receive a larger compensation than player 2 (i.e., contest/exchange), (a) player 1 will offer significantly less to player 2; while (b) player 2 will accept any given offer with higher probability. The data in Figure 1 are consistent with prediction (a) and not inconsistent with prediction (b). Player 1s offer significantly less to player 2s, while rejection rates are statistically indistinguishable. These results suggest that the change from random/divide to contest/exchange alters the shared expectations of the two players regarding the social exchange norm operating to determine an appropriate sharing rule. Finally, the difference between random/divide and contest/exchange carries over to dictator experiments as well, indicating that the change in expectations takes place even when there is no threat of punishment from player 2.

But why do these treatments reduce offers without causing an increase in the rejection rate? One hypothesis is that both players infer one anothers' mental states - in this case expectations - from relevant information in the experiment. "Mind reading" implies the ability to take the perspective of another person who has common information. In this experiment, player 1 expects player 2 to find a lower offer acceptable, while player 2 expects, and is prepared to accept, a lower offer. At minimum, this involves a shared attention mechanism.

Observability is potentially powerful in the enforcement of social norms. Thus, FHSS recruited Player 1s and Player 2s in separate rooms, and the players were anonymous with respect to one another. However, subject decisions were not anonymous with respect to the experimenter. Someone was still "watching"; hence player Is were still not entirely removed from a social exchange setting where reciprocity norms might unconsciously apply.

This led HMSS to design a "double-blind" dictator experiment, with several features that were later changed one or two at a time, to investigate the role of social isolation in extinguishing behavior reflecting social norms (Hoffman, McCabe and Smith [1996a]). In the double-blind treatment, 64% of the Player 1s take all $10; about 90% take at least $8.(6)

These results are strikingly different from the dictator results in FHSS, and from the HMSS random/divide and contest/exchange dictator experiments in which subjects were observed by the experimenters. Next, in three stages, HMS vary each of the elements of the double-blind dictator experiment in ways intended to reduce the "social distance" between the subjects and anyone who might see their choices. The experimental results form a predicted ordered set of distributions. As the social distance between the subject and others decreases, the cumulative distribution of offers to Player 2s increases. These results demonstrate the power of isolation from implied observability in the enforcement of norms of equality, equity and reciprocity.

Signaling, Trust, and Punishment in Bargaining Experiments

In this section we review the results of two-person extensive form bargaining/trust experiments in which players move sequentially, and one player can choose to play - signal - cooperatively. Berg, Dickhaut and McCabe [1995] have adapted the double-blind procedure to study trust and reciprocity in a two-stage dictator game. In stage one player 2 decides how much of $10 to send to player 1, and how much to keep. The amount sent triples to M before reaching player 1. In stage two player 1, acting as a dictator, decides how to split the M dollars. Since the amount to be split is endogenous, the two players now share a common history before the dictator game is played. If reciprocity plays a significant role in promoting social exchange, then their common history should reduce the "social distance" between subjects in a two-stage dictator game. While Berg, Dickhaut and McCabe find significant use of trust and reciprocity, subjects in their experiments had no alternative except to rely on trust for mutual gain.

McCabe, Rassenti and Smith [1996a] study an extensive form game in which a player can choose between two subgames, each of which can result in mutual gain. In one subgame mutual gain can be achieved using reciprocity incentives, while in the other subgame mutual gain is achieved using self-interested incentives. By choosing the reciprocity subgame the subject signals a desire to cooperate, and each subject can earn 50. By choosing the self-interested subgame the subject signals a desire to play noncooperatively, and each subject earns 40. In some of these experiments, the signaling player, at a cost to himself or herself, can directly punish the other player for "cheating" on the implied social exchange. In the other "trust" experiments, there is no direct opportunity to retaliate against defection from a signal to cooperate.

The Constituent Games: Payoffs. Figure 2 shows the extensive form bargaining tree for these two constituent, or stage, games played by two persons. Player 1 begins with a move right or down at node [x.sub.1]. A move right terminates the play with payoffs (35, 70), in cents, in repeat play (multiplied by 20 in single play), respectively for Players 1 and 2. If the move is down, then Player 2 moves left or right at node [x.sub.2], and so on. Play ends with any move that terminates at a payoff box on the right or the left of the tree. Game 1 shows the baseline payoff structure used; Game 2 is the same except for the payoffs in the boxes corresponding to plays left at nodes [x.sub.3] and [x.sub.5]. McCabe, Rassenti and Smith [1996a] have studied behavior in these games under a variety of matching protocols and information treatments.

In both Games 1 and 2 the right side of the tree contains the subgame perfect (SP) noncooperative outcome (40, 40), where Player 2 moves right at [x.sub.6]. This outcome is achieved by simple dominance, once Player 2 moves right at [x.sub.2]; i.e., it is in Player 1's interest to play down at [x.sub.4], and for Player 2 then to play right at [x.sub.6].

In Game 1, cooperative actions by the players can lead to the largest symmetric (LS) outcome (50, 50), achieved if Player 1 moves left at [x.sub.3]. Under complete payoff information, a move left at [x.sub.2] by Player 2 can be interpreted as a signal to Player 1 that Player 1 should go left at [x.sub.3]. (This is because 50 at LS is clearly better than 40 at SP for Player 2, allowing Player 1 to infer Player 2's reason for playing left at [x.sub.2].) Player 1, however, can defect, move down at [x.sub.3], and force Player 2, in his or her own interest, to move left at [x.sub.5] giving Player 1 a payoff of 60. In fact this is the game theoretic prediction if play occurs on the left side of the tree in Game 1. In a single play, Player 2 should see this and the theoretical prediction becomes Selten's SP outcome on the right.

But a move left at [x.sub.2] in Game 1 is more than a signal that Player 2 wants to achieve the LS outcome (50, 50). It can also be interpreted as a potential threat to play down at [x.sub.5], punishing Player 1 if Player 1 defects or "cheats" by playing down at [x.sub.3]. This action, however, is costly to Player 2, since each player gets 20 if Player 1 moves left at [x.sub.7]. But, given the way subjects behave in ultimatum games, it is not unreasonable to assume that some subjects will move left at [x.sub.2] and then punish defections at [x.sub.3].

Game 2 contrasts with Game 1 in that to achieve LS, by Player 2 moving left at [x.sub.5], Player 1 must resist the temptation to move left at [x.sub.3]. In Game 2, Player 1 can "cheat" on the invitation to cooperate by choosing (60, 30) without the prospect that Player 2 can punish Player 1. Thus, Game 2 allows signaling, but not punishment; it is a game of trust.

Experimental Design. Table I shows four treatments that vary the protocol for matching pairs in each experiment. An experiment consists of groups of 8-16 subjects who are randomly assigned to pairs. In Repeat Single we begin the session with 16 subjects, and each person plays every other counterpart once, with their roles alternating between Player 1 and 2. Under Contingent each player indicates her choice at each node. Then the computer executes the play. Single means that all pairs play the constituent game exactly once for a multiple of 20 times the payoffs shown in the boxes of Figure 2.

Summary of Results. Table II lists the conditional outcome frequencies for each payoff box. Reading across data row 1 for Single 1 we observe that 13 of 26 Player 2s moved left at [x.sub.2] indicating cooperation; 10 of the 13 left plays ended with Player 1 choosing (50, 50); three Player 1s defected by playing down at [x.sub.3]; two of these Player 2s accepted the defection and responded with (60, 30), while one played down at [x.sub.5] to punish Player 1 who then chose (20, 20). In the right game, played by 13 of 26 Player 2s, 12 of 13 ended at the SP outcome (40, 40); one play was at (15, 30). The column labeled E([Pi]2[where]Left) computes the expected profit, 44.6 cents, to player 2 from playing left at [x.sub.2], based on the relative frequencies of subsequent play by both players. E([[Pi].sub.1][where]Down) is the expected profit, 46.7 cents, to Player 1 from defecting at node [x.sub.3]. Efficiency is the percentage of the cooperative total payoff at (50, 50) that is realized by all players. Thus in Single 1 85.5% of the cooperative surplus is collected by all pairs. At SP efficiency is 80%, so any greater efficiency implies a net social benefit from cooperative initiatives.

[TABULAR DATA FOR TABLE I OMITTED]

Result 1. Game theory predicts that in Single 1 all plays will be in the right subgame. In fact half are in the left subgame. In Repeat Single 1, we observe that experience does not help to achieve SP; now 58% play the left subgame. Contrary to the theory, we observe both too much attempted cooperation and too few defections on these attempts. Conditional on right-branch play however, game theory does very well in predicting the SP outcome for both Game 1 and Game 2 in all treatments.

Result 2. In all treatments it is (weakly) advantageous in the expected payoff sense to play in the left subgame. This is indicated by the fact that the expected profit to Player 2 of left-branch play is at least 40.0 cents in all treatments, and 40 is the payoff to Player 2 at SP. Thus, right subgame play by the minority is not profitable in both Games 1 and 2.

Result 3. Defections by Player 1 at node [x.sub.3] of Game 1 are not profitable under the Single 1 and Repeat Single 1 treatments: the expected profit of playing down is always less than 50, the payoff to Player 1 by not defecting. Thus, the "punish cheaters" mental module hypothesized by Cosmides [1985] is alive. Moreover it is used only just enough to be effective, but not so much that efficiency is badly compromised.

Result 4. Single 1 Contingent converts Game 1 from the extensive to the normal form by requiring each player's choices at all nodes of the tree to be made in advance for simultaneous play. It is equivalent to expressing all payoff path outcomes in matrix form for simultaneous choice by both players. Game theory hypothesizes that the normal and extensive forms are equivalent, but previous research has shown that this is not generally the case (Schotter, Wiegelt and Wilson [1994]). Comparing Single 1 with Single 1 Contingent we see that left play declines (right play increases) in the latter. Why? Our hypothesis is that the extensive form, with sequential turntaking moves, allows the players to engage in a move interpreting conversation. Thus, at node [x.sub.2], Player 2 has just received the message, "I moved down at [x.sub.1] because I want to do better than receive 35," from Player 1. If Player 2 now moves left, the message is "I am playing left because I want to forgo the (40, 40) on the right in favor of (50, 50) which is better for both of us. Also, note that if you respond by playing down at [x.sub.3], then I have the option of punishing you with (20, 20)." This hypothetical dialogue is disrupted with simultaneous play, although under strict rationality it is irrelevant: Player 2's message is not credibly self enforcing. But as we have seen (Baron-Cohen [1995]), mindreading allows players to infer mental states from actions and, as shown by these results, may lead them to play differently in the extensive form than in the normal form.(7)

[TABULAR DATA FOR TABLE II OMITTED]

Result 5. The failure of the SP predicted outcome (Result 1) motivated the study of Game 2 in which the cooperative (50, 50) outcome cannot be supported by the prospect of punishment. Comparing Single 2 with Single 1 (rows 2 and 1 of Table II), we see a slight reduction in left moves by Player 2s in Game 2. Play in left subgame 2 produces fewer (50, 50) outcomes (50%) than in Game 1 (76.9%). This reduces the expected profit of left play from 44.6 cents in Game 1 to a break-even 40 cents in Game 2. Clearly, the strategic difference between the two games is making a difference in the game theoretic predicted direction. The more interesting observation is that the trust element in Game 2 is sufficient to yield cooperation for half of the pairs who play the left subgame. This is consistent with results reported by Fehr, Kirchsteiger and Riedl [1993] in labor market experiments, and by Berg, Dickhaut and McCabe [1995] in investment dictator games. In these studies first movers trusted second movers to reciprocate with no possibility of punishment.

If you think of noncooperative game theory as applying to "foes," in these extensive form experiments the theory accurately predicts behavior in up to half the observations. The relevance of traditional game theory for a large segment of this population cannot be dismissed. However, the other half, who persist in cooperation, need also to be explained and modeled. Their behavior is not extinguished with experience: in Repeat Single 1, the percent of play in the left reciprocity branch increases to 58%. We conjecture that minimal elements for a complete theory of mental phenomena in games of strategy should include: (1) a friend-or-foe detection mechanism, and (2) an intentionality detector mechanism, where the latter requires extensive form play to achieve its full scope.

V. WHEN DO PEOPLE ABANDON RECIPROCITY IN FAVOR OF NONCOOPERATIVE PLAY

The above examples illustrate a model of a mixture of individuals, some of whose play reflects game theoretic principles, while others' play reflects learned or innate responses involving signaling, trust, punishment and other ingredients of reciprocity behavior. In the latter, the play objective serves the typical subject well: they exceed the performance of strict game-theoretic players in that surplus-improving cooperative outcomes are more often attained than theory would predict.

In this section we consider a contrary example to those above, one in which subjects begin with their intuitive automatic responses, discover that these responses cannot sustain good performance, then adjust in the direction of the noncooperative rational expectations outcome predicted by theory. In this case subjects are given common information, but this is not sufficient to induce common knowledge in the sense of expectations. (Also see Smith, Suchanek and Williams [1988] and Harrison and McCabe [1992]). This, we argue, is because common information leaves behavioral or strategic uncertainty unresolved. The latter is resolved over time as subjects, in successive extensive form rounds, come to have common expectations that predicted equilibrium outcomes will prevail.

McCabe [1989] reports a six person, six period, extensive form game experiment using fiat money. In successive periods subjects use buy, sell and null messages to trade, or not trade, a unit of fiat money against cash dividend paying bonds. In the last period a bond holder should not sell since he or she is left with worthless fiat money. Similarly, the money should not be accepted on the penultimate round, and by backward induction should not be accepted in the first period. Although subjects have complete information on this payoff structure, trade in the first play of the sequence yields trade in each period until the last one. Repeating this constituent game 10 times (common information) causes some, but not a complete, unravelling backward from the final trial. When subjects return for a second 15 trial experiment, the slow unravelling process continues, but trade persists, especially in the early trials. In a third session for 20 trials, gradually, trade is further diminished, and is virtually eliminated by the 15th trial.

These results can be understood in terms of a model in which people have been strongly conditioned by reciprocity experience to accept flat money in trade because they expect others to accept money when they offer it in trade. This expectation is unconscious; they never ask themselves why they and others accept money. It is a conditional reciprocity response, which serves them effectively in daily life. They are recruited to the laboratory where the conditions for ongoing repeated exchange are not satisfied; in the end-game intrinsically worthless money is refused in trade. This failure experience induces them to reevaluate their unconscious, accustomed response to money. Very slowly, in the limit, as play is repeated in the finite horizon environment, trade converges to zero.(8)

VI. CONCLUSIONS

The experimental game results summarized in this paper suggest that people invoke reward/punishment strategies in a wide variety of group interactive contexts. These strategies are generally inconsistent with, but more profitable than, the noncooperative strategies predicted by game theory. However, in contrast to CT's emphasis on punishing cheaters, we observe substantial use of positive as well as negative reciprocity strategies, even in single-play games. Hence behavior is much richer and more trusting than CT's model would predict.

A punish-cheaters mechanism has the advantage, as in tit-for-tat, that it can sustain cooperation. But is a pure trust/trustworthy mechanism sustainable? Recall that the "cooperate" strategy C in the PD game cannot resist invasion by defectors. This is still an open question, but Carmichael and MacLeod [1997] offer a model which is encouraging. They analyze gift exchange showing that a stable gift-giving custom, which does not depend upon the use of punishment strategies, may emerge.

Consider the following hypothetical model of the mind for human decision making. We inherit a circuitry which is modularized for solving social exchange problems. But the switches are not set; that occurs sometime in our maturation, requires no formal instruction, and is not a self-aware process. In this sense it is like the way we "learn" natural language without being taught. The switches are set differently in different cultures, but the results are functionally equivalent across cultures; in particular there is a propensity to be programmed to try cooperation in dealing with other people who are not detected as foes. But there is variation so that we can talk about population distributions of P, the probability that a person will initiate cooperation, of Q, the probability that a person will defect on an offer to cooperate, of R, the probability a defection will be punished, of S, the probability that a person will be trusting, of T, that a person will be trustworthy, and so on. These distributions of player types are an adaptation capable of changing slowly over time.

Formal education is hard because it is concerned with conscious learning, expression, and action, and does not come naturally, just as written language is unnatural and hard to learn. When people are exposed to economic principles, most find it extremely hard to learn about comparative advantage, opportunity cost, gains from exchange, and Nash equilibria. Many give up, but it does not follow that if they are in an economics experiment that they will perform poorly. This is because they may be good at reading other minds and relying on their unconscious natural mental mechanisms. These mechanisms help to define reputations that are applied repeatedly across different life, and laboratory, games. A one-shot game in the laboratory is part of a life-long sequence, not an isolated experience that calls for behavior that deviates sharply from one's reputational norm. Thus, we should expect subjects to rely upon reciprocity norms in experimental settings, unless they discover in the process of participating in a particular experiment that reciprocity is punished and other behaviors are rewarded. In such cases they abandon their natural instincts, and attempt other strategies that better serve their interests.

We are grateful to the National Science Foundation for research support under NSF #SBR-9210052 to the University of Arizona.

1. But see Rice [1996] for an experiment in which female fruit flys are prevented from coevolving with males. After only 41 generations male adaptation leads to a reduction in female survivorship in the genetic battle of the sexes.

2. Research by neuroscientists on the amygdala, an almond-sized structure deep in the temporal lobe of the brain, has shown that it is directly involved in the perception of social signals. That the amygdala participates in the social cognition and behavior of animals has been known for many years, but recent studies have shown that these findings extend to humans (Allman and Brothers [1994] Adolphs et al. [1994]). Thus, subjects with damaged amygdalas are unable to recognize or distinguish expressions such as fear, surprise and anger on faces in photographs of people. In one study, the subject had great difficulty determining whether individuals were looking at her or away from her. The amygdala operates preconsciously: "the evidence ... clearly indicates that the amygdala is involved in the evaluation of complex stimuli long before they are completely analyzed cognitively, and probably long before they enter awareness" (Halgren [1992, 194]).

3. Pinker [1994, 227] for example provides the following exchange: Woman: "I'm leaving you." Man: "Who is he?" If you are not autistic you know what this conversation means.

4. Unlike deductive logic, a cheater detection mechanism must account for intentionality. In the CT experiments exchange is sequential: first, I give you the watch, then only later do you pay the $20. Here the clear interpretation is that the second mover has cheated if he or she does not pay the $20. This rules out the use of the biconditional statement, "You give me your watch," if and only if, give you $20," as a substitute for the conditional. Since the biconditional has an ambiguous intertemporal interpretation, it is less clear that a contract is implied. Suppose I give you $20, but you don't give me your watch. The biconditional is clearly false even if I haven't cheated you; when, for example, I give you the $20 altruistically. Note we can write the more complicated logical statement, if (we agree to P iff Q), then (P iff Q), to give the biconditional the correct intertemporal interpretation without committing to the order of trade.

5. Other experiments have examined violations of social contracts when they do not involve cheating (Gigerenzer and Hug, cited in CT [1992, 195]. Only 44% correctly solve the no-cheating version, while 83% get the cheating version correct. Cosmides and Tooby (in preparation, cited in CT [1992, 198]) have examined social contract problems which distinguish violations due to cheating from violations due to innocent mistakes. The cheating version is correctly solved by 68% of the subjects, but the mistake version is only solved by 27% of the subjects. Other social contract reasoning tasks asked subjects to detect altruists instead of cheaters. People are not good at detecting altruists. In fact where the rule was a social law (public good) more people detected cheaters than altruists (CT [1992, 193-95 and footnote 17]).

6. Bolton, Katok and Zwick [1993], using a different version of the dictator game and using different doubleblind procedures, find no difference between their doubleblind and single-blind treatments. The results from such treatment variations are always of interest, but claims that the experiments show that the results of HMSS do not replicate exceed what is demonstrated. When examining treatment variations on an earlier study, a second experimenter must first show that he/she can duplicate the original results using the same treatment and procedures, establishing that the results replicate with different subjects and different experimenters. Only then can the results using the new treatment, if different, be attributed to these conditions and not to the subjects, experimenter, or procedures used. Thus, HMSS replicated the procedures and results of Forsythe et al. [1994] before attempting to compare them with the results from new treatments. Given the sensitivity of the dictator game to procedures and instructions, it is important that other researchers be able to replicate such findings before changing the treatment. Eckel and Grossman [1996] replicated the HMSS double-blind experiments before conducting their interesting new treatment in which the recipient was the American Red Cross instead of another subject. Terry Burnham also replicated the HMSS double-blind experiments in a study currently in process (private communication).

7. Additional tests of the reciprocity hypothesis based on comparisons of the extensive form with matrix normal form are reported in McCabe, Smith and Lepore [1997]. The reciprocity hypothesis also implies that SP outcomes will predominate under private information. This prediction is strongly supported in McCabe, Rassenti and Smith [1996b].

8. Similarly, Camerer and Weigelt [1988] report very slow convergence in a sequential equilibrium reputation model.

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Hoffman, Elizabeth: Provost and Vice Chancellor for Academic Affairs, and Professor of Economics, History, and Psychology, University of Illinois at Chicago, Ill., Phone 1-312-413-3450, Fax 1-312-413-3455, E-mail ehoffman@uic.edu

McCabe, Kevin A.: ESL Senior Research Scholar, Professor of Economics, and IFREE Distinguished Research Scholar, Economic Science Laboratory, University of Arizona, Tucson, Phone 1-520-621-3830, Fax 1-520-621-5642, E-mail kmccabe@econlab.arizona.edu

Smith, Vernon L.: Regents' Professor and McClelland Professor of Economics, Economic Science Laboratory, University of Arizona, Tucson, Phone 1-520-621-4747, Fax 1-520-621-5642, E-mail smith@econlab.arizona.edu