Asymmetric power relations and cooperation in anarchy.

Sutter, Daniel

Anarchy as an organizing principle for society must appeal to anyone who places individual freedom on his scale of values.... It is not surprising that "anarchy" and "anarchism" have re-emerged as topics of discussion in the 1960's and the 1970's, as tentacles of government progressively invade private lives and as the alleged objectives of such invasions recede yet further from attainment.

Winston Bush [5, 1]

I. Introduction

The political system of anarchy generates strong responses (positive and negative) from scholars. Conflictual and cooperative visions of anarchy coexist. The most famous proponent of the former view is Thomas Hobbes, who depicts the state of nature as a war of all against all where life is "solitary, poore, nasty, brutish, and short" [17, 186]. The Hobbesian vision has dominated the discussion of anarchy, which for many is a synonym for chaos.

I consider the prospects for cooperative anarchy within the institutional framework of anarcho-capitalism in which private, for-profit agencies offer sets of legal codes and enforcement of these codes. In anarchy no institution exists with legitimate authority over all members of society. Many situations resemble anarchy in this respect, including international business and trade, relations between nations, the informal (black market) sector of controlled economies, the underground (criminal) sector, political promises and deals, and constitutional (or social) contracts. Cooperation is not unknown in such situations. The Merchant Law in early medieval Europe [2] and the Maghribi traders' coalition [12] are examples of institutions that enable cooperation. These examples suggest Hobbesian vision underestimates the possibilities for cooperation in anarchy.

I proceed as follows. Section II discusses the literature on cooperation in anarchy and elaborates on the nature of anarcho-capitalism. The key issue for the effectiveness of anarcho-capitalism is the distribution of property rights. Section III models the relationship between individuals and protection agencies. I illustrate how this asymmetric power relationship might be biased in favor of the agencies, which could degenerate into exploitative gangs. Section IV considers a number of extensions to the model which allow the allocation of rights between individuals and agencies to be relatively equitable, and is the main contribution of this paper. Section V concludes by examining asymmetric relations in actual anarchic situations. Anarcho-capitalism itself has never been implemented. Competition between governments, however, does occur. This and several other situations sufficiently resemble my model to provide relevant evidence and illustrate the general applicability of this research. I find evidence of mixed effectiveness of the devices discussed in section IV.

II. The Emergence of Property Rights and Cooperation in Anarchy

Government performs two tasks which facilitate market exchanges: it secures individuals' initial possessions, and it enforces agreements made by individuals. In some anarchic situations initial possessions are secure but government-enforced contracts are unavailable. Many scholars have examined how spontaneous (or market) forces, through the means of reciprocity, reputation, and hostages, can readily substitute for government enforcement in this circumstance.(1) Conditions which facilitate cooperation include repeated interaction between a set of parties, a low discount rate on the part of all parties, and the ability to recognize and identify trading partners.

Several anarchic situations, including anarcho-capitalism, lack both enforceable agreements and secure initial possession. In the absence of government, spontaneous forces have to fulfill both tasks. If stable property rights can be established, reciprocity and reputation indicate economic activity could flourish in anarchy. But can secure property rights be provided in the absence of government?

A small but growing body of research examines the emergence of property rights in an-archic situations. These models emphasize the allocation of power among individuals and the effectiveness of predatory action in determining the allocation of property [6; 16; 32; 33; 36; 37]. The distribution of rights depends critically on the balance of force: "... all private ownership rights are ultimately founded on the ability to forcefully exclude potential competitors. Force, not fairness, determines the distribution of wealth in a society" [36, 57]. Although models of the emergence of property rights focus primarily on symmetric conflict situations, the implication for asymmetric situations is that the stronger party dominates.(2)

I consider the implications of this research for cooperation in the anarcho-capitalism model of anarchy,(3) which represents the total privatization of government. For-profit agencies offer a set of legal codes and protection and enforcement of these codes. Agencies may differ in the "laws" they offer; for example, agency A may include gambling and prostitution as "crimes" and enforce the death penalty for some offenses while agency B might not. Agencies may also differ in the level of protection and enforcement of their codes; A may rely on padlocks and alarms to protect clients' homes and businesses while B may offer armed guards. People choose the agency that most satisfies their preferences for laws and enforcement.

The parallel with consumer choice in the market is at the core of the intuitive appeal of the system. The power of competition (hopefully) forces for-profit agencies to be more responsive to consumer preferences than bureaucratic, monopoly government. The system relies on the ability of reputation and reciprocity to allow contracting between individuals and agencies and to facilitate interagency relations. If the analogy to freedom of choice within the market place is inappropriate, the system is unlikely to perform as advertised.

Will people be able to choose which agency to patronize in anarcho-capitalism? Market exchange occurs within a political system which enforces property and contract rights. In anarcho-capitalism there is no corresponding institution. Freedom to choose must arise as an outcome within the system. Unfortunately, the advocates of anarcho-capitalism do not adequately tackle how freedom of choice is attained as an equilibrium of the system.

The problem of securing initial possessions is different from providing enforceable agreements. Reputation and reciprocity work only after the former task is accomplished. The distribution of force among participants is crucial in the emergence of stable property rights. In anarcho-capitalism the key relationship is between the protection agency and the individual, which is asymmetric. As a consequence, the resulting distribution of rights may be highly skewed, with no effective freedom of choice between agencies for individuals. Since personal freedom is an important normative criterion for anarcho-capitalists, such a negative result is very damaging.

Must the protection agencies necessarily degenerate into exploitative gangs? Or might spontaneous forces be able to provide effective protection to the rights of individuals? I address this question in section IV, which represents the major contribution of this paper.

To facilitate examination of the relationship between individuals and agencies I accept uncritically several features of anarcho-capitalism worthy of consideration in a more general study. I assume more than one protection agency exists and that agencies do not collude. I do not examine which laws and enforcement procedures agencies offer potential customers. The issue of interagency relations and dispute resolution is ignored entirely (i.e., what happens when a client of A is accused of an offense against a client of B). The internal structure of agencies and the effects of the system on economic performance are not examined.(4)

IIl. A Model of Anarcho-Capitalism

A population of many individuals inhabits a given region with m ([greater than] 1) existing protective agencies. Let M be the set of agencies, M = {1,..., m}. Each individual is either a client of one of the agencies or is independent. Clients of an agency make payments in exchange for protection services. Let v [is greater than] 0 be the profit an agency makes on the typical individual.(5) I consider an agency A and an individual d who does not wish to be a client of A. Let s [is greater than] 0 be the value to d of not patronizing A, either to remain independent or be a client of agency B. The reasons for d's preference are immaterial but may include the laws offered by A. Any differences in the products (laws and services) offered by agencies are assumed not to affect the per client profit. The efficient outcome in each of the games of this section is for d not to become or remain a client of A.

For simplicity I describe the relationship between agencies and individuals as if the former were genuinely offering protection services to their clients. The model can be interpreted in strictly exploitative terms if the reader wishes. The amount v, for example, then is the net value of wealth expropriated from d. Protection agencies are motivated by profit and implement any strategy which increases profit whether violent or not. Moral standards affect the activities of protection agencies only through consumer response (if any) to brutality.

The assumption v [is greater than] 0 imposes that the market structure for protection services is oligopolistic.(6) The protection market would likely not be perfectly competitive for several reasons. First, economies of scale in providing protective services are likely. Agencies need to attain a minimal size to be able to successfully confront other agencies; this limits the number of agencies and creates a barrier to entry. Second, reputation effects, stressed in the operation of anarcho-capitalism by the authors mentioned, are inconsistent with perfect competition. Once agencies have reputations they no longer supply a homogeneous product in the eyes of consumers.(7)

One person is small relative to any existing protection agency. An agency always wins a confrontation with an individual and this is common knowledge. The confrontation has negligible cost to the agency while the individual suffers a large cost P. An agency may fine a client who attempts to exit an amount p ([is greater than or equal to] 0) which can only be collected if the attempt fails.

Confrontations between protection agencies are skirmishes which do not threaten the existence of the losing agency and are costly for both the winning and losing sides. The outcome and costs are functions of the size of the protection agencies. For simplicity, assume strength is proportional to agency size and agencies do not differ in their ability to produce strength. Let q(j) be the number of clients of agency j. The probability of victory for agency j in a confrontation with k is [Alpha](q(j), q(k)). Assume [Alpha]([center dot], [center dot]) [is an element of] [0, 1] is increasing in q(j) and decreasing in q(j[prime]).(8) Let D([center dot]) be the cost of winning a confrontation as a function of the size of the defeated agency and L([center dot]) the cost of losing a confrontation as a function of the size of the victorious agency. Both D([center dot]) and L([center dot]) are increasing and for all q [is greater than or equal to] 0, L(q) [is greater than] D(q) [is greater than] 0.

The Protection Racket Game examines relations between A and d. The game is illustrated in Figure 1. The interaction depicted occurs either when A attempts to win the patronage of an independent d or when d attempts to leave A. Assume that once confronted by A an individual is unable to flee to avoid confrontation, or equivalently an agency may always challenge an exiting client. The payoffs of the game are as follows. A receives v if d becomes a client. d receives s if she does not end up a client of A and -P if involved in a fight with A. The unique Nash equilibrium (in pure and mixed strategies) is

NE = {(d = Accept, A = Confront)}, (1)

so d becomes a "customer" of A. Agencies do not have to bargain with independents to win their patronage. Alternatively, an individual cannot end a relationship with a protection agency even if it were voluntarily entered into. The equilibrium illustrates how the allocation of rights between protection agencies and individuals in anarcho-capitalism may favor the agencies.

IV. Prospects for Equal Treatment of Individuals

Several unrealistic assumptions were made in section III to highlight the asymmetry between individuals and agencies. The relaxation of these assumptions on the whole weakens the position of the agency. I assumed an agency could costlessly and with certainty challenge any individual. More realistically the probability A can challenge an exiting d is a function of the resources A spends on fences, guards, etc. If these inputs are not sufficiently productive, they may not be a worthwhile investment for A. In equilibrium the probability of interdiction will generally be less than one, so exit is not totally foreclosed. An exit attempt may be rational for individuals even if there is a chance of being caught. Also a confrontation with an individual imposes some costs on an agency because some employees will be injured and equipment damaged in a lopsided fight. It may not be cost-effective for A to fight d, even if the outcome is not in doubt. Together these additions ensure some mobility exists in anarcho-capitalism. Exactly how much and whether it is sufficient to induce competition among protection agencies are interesting questions, though beyond the scope of this paper.

The analysis of section III suggests anarcho-capitalism may resemble a market with switching costs. Klemperer [19] shows the equilibrium of a competitive market with switching costs mimics the collusive oligopolistic equilibrium. Two factors which increase competition in a switching cost model are first period competition for customers before they become "locked in" and entry of new customers to the market after the first period [19; 20]. My analysis suggests each of these factors would be weak in anarcho-capitalism. Once agencies become sufficiently large, they do not have to "compete" for unaffiliated customers - they can coerce patronage. Since individuals cannot remain independent, there is no pool of potential new customers in a future period. Additionally children could enter adulthood locked in to their parents' agency. The only source of new clients in a future period is migration into the region.

Since d values exiting A, following the logic of the Coase Theorem, she might purchase her freedom. With only two parties involved, transactions costs would be low. Coasian sidepayments are unlikely to work effectively in anarcho-capitalism for several reasons. Credit markets may be imperfect or individuals may be wealth constrained. Most importantly the freedom thus purchased would not be credible; d and A would return to the situation of the Protection Racket game and the cycle could begin anew.

An individual was unable to leave her current agency in the Protection Racket Game. Since an individual is weak relative to an agency, help is needed to exit. A profit-motivated agency could possibly provide this assistance. The Exit Game examines when d, currently a customer of A, attempts to switch to a rival agency B. A person may wish to leave her current agency for several reasons, including that she was "recruited" as in the Protection Racket Game. I again assume that A can contest the exit attempt if desired with certainty and at zero cost; also that the cost to d of moving is zero. A game tree illustrating the Exit Game is contained in Figure 2. The game has three players, d, A, and B. d moves first and attempts to defect. A next decides to allow or contest the defection. B then decides whether to backdown or confront A, in which case there is a battle. If B backs down, d abandons the exit attempt and returns to A, which fines d an amount p [is greater than or equal to] 0. If them is a battle, d ends up a client of the victorious agency.(9)

The payoffs of the Exit Game are as follows. If d does not exit or if B backs down, A and B receive a payoff of 0; d is fined and injured if she exits and B backs down. If A allows exit, v is transferred from A to B while d receives the benefit s of escaping A. If A and B battle, d is fined if A wins or receives benefit s if B wins. A and B suffer damage from the fight and v is transferred if B wins.

Analysis of the game focuses on play in the subgame between A and B which occurs if d announces an intention to defect to B. The Nash equilibria in pure strategies for the subgame are:

NE = {(A = Contest, B = Backdown), (A = Allow exit, B = Confront)}. (2)

The following conditions ensure the strategy combinations in (2) are Nash. They imply the costs of a battle are larger than the profit the agency earns from the typical client.

-D(q(A)) [is greater than] v (to ensure [z.sub.3] [is less than] 0); (3)

-D(q(B)) [is greater than] v (to ensure - [z.sub.2] [is greater than] v). (4)

In the second equilibrium of (2) d is able to defect from A to B. The addition of a rival agency can allow for free exit by individuals even given the strict assumptions of the Exit Game. As a result, the allocation of rights between individuals and agencies would, in this equilibrium, be relatively equal. The existence of a no exit equilibrium in (2) is, nonetheless, a serious threat to the viability of anarcho-capitalism. If protection agencies need not cater to consumer preferences the performance of the system is likely to be poor. The existence of a dismal equilibrium is probably sufficient to induce all but its strongest supporters to dismiss anarcho-capitalism. So I seek further means by which the rights of individuals could be protected in the no exit equilibrium of the Exit Game.

The rival agency has a greater incentive to confront A if a group of clients attempts exit. Let k be the number of clients of A seeking to exit to B. Since k must be small relative to the size of A to remain within the context of the model, the effect on q(A) and q(B) is ignored. Payoffs for A and B as functions of k are

[z.sub.2](k) = -[Alpha] [center dot] D(q(B)) + [1 - [Alpha]] [center dot] [-L(q(B)) - k [center dot] v], [z.sub.5](k) = -k [center dot] v; (5)

[z.sub.3](k) = -[Alpha] [center dot] L(q(A)) + [1 - [Alpha]] [center dot] [-D(q(A)) + k [center dot] v], [z.sub.6](k) = k [center dot] v. (6)

The rank orderings of the payoffs for A and B can change as k increases. Examination reveals that A's payoffs, [z.sub.2](k) and [z.sub.5](k), are decreasing functions of k while B's payoffs, [z.sub.3](k) and [z.sub.6](k), are increasing functions of k. As long as [Alpha] [is greater than] 0, [z.sub.6](k) [is greater than] [z.sub.3](k) for all k, but when k is sufficiently large, [z.sub.3](k) [is greater than] 0. Confront then becomes a (weakly) dominant strategy for B. Exit in groups may possibly rescue freedom of exit (contract). When k is sufficiently large, however, [z.sub.5](k) [is greater than] [z.sub.2](k). The net expected value to A of a confrontation with B is then positive; exit in groups may give A an incentive to fight to prevent exit.

Four cases are possible depending on the ordering of [z.sub.3], [z.sub.2], and [z.sub.5]. In one case, [z.sub.3](k) [is greater than] 0 and [z.sub.5](k) [is less than] [z.sub.2](k), the unique equilibrium of the subgame between A and B is (A = Allow Exit, B = Confront). Freedom of exit for individuals in groups is protected here. A necessary condition for this case is that q(B) [is greater than] q(A) so only the strongest agencies benefit from exit in groups. Exit by groups over time may increase market concentration and is at best an imperfect means of providing freedom to contract.

A further generalization of the Exit Game incorporates that while some clients wish to defect from A, some from other agencies will want to join A. Protection agencies may have an incentive to allow their clients to exit in exchange for similar guarantees from other agencies. I examine conditions under which this might occur.

The subset of agencies currently cooperating is called a coalition and designated C. Assume agencies which cooperate in this manner agree (i) to allow their clients who wish to defect to other members of the coalition to do so; and (ii) not allow their clients to defect to the agencies outside the coalition. All other agencies not in C are assumed in the no exit equilibrium of the Exit Game. The "coalition" is for analytical purposes; actual cooperation need not be formally organized or chartered at all. At any time assume there is only one active coalition. If C = M, full freedom of choice for individuals exists. If the protection agencies are exploitative gangs, the movement described here could be a slave trade.

Let [Pi](j) be the probability a client of agency j = 1,...,m wishes to defect from j during the period under consideration. The expected number of j's clients wanting to defect is F(j) = [Pi](j) [center dot] q(j). Let [Beta](l; j) be the probability that an agent who wishes to leave j wants to join agency l. Then [summation of] [Beta] (l; j) = 1 where l [is not equal to] j and the expected number of defectors from j to l is [Beta](l; j) [center dot] F (j).

The behavior of individuals is now summarized in [Pi](j) and [Beta](l; j). Assume when an individual switches from agency A to B that B is able to perfectly price discriminate and capture all the benefit (s) of the switch. This extreme assumption is the upper bound on revenue an agency could expect from a new client and simplifies analysis.

An agency joins C if its expected net payoff from membership is positive. The payoff to j from membership in C, W(j; C), is

[Mathematical Expression Omitted].

Each agency would be willing to join M as a coalition if

[Mathematical Expression Omitted].

for each j [is an element of] M.

The numerator of the RHS of (8) is the number of clients expected to defect from agency j to other agencies while the denominator is the number of now clients agency j can expect to gain from other agencies. The ratio of lost to new clients cannot exceed (s + v)/v.

If (8) does not hold, full freedom of contract will not arise. (8) is less likely to hold if: i) an agency j is large; ii) an agency is particularly likely to lose clients; iii) an agency is not likely to gain new clients; and iv) profit per typical member v increases. The final condition implies freedom of contract is less likely to arise if the market for protection is concentrated.

A particularly exploitative agency is relatively unattractive to consumers. Its ratio of desired defectors to potential newcomers would be very high so (8) is unlikely to hold for such an agency. Cooperation is therefore unlikely to involve the worst (from the consumers' point of view) agencies.

Two factors diminish the possibility of cooperation described here. First, the probabilities [Pi](j) and [Beta](l; j) may not be known by all agencies. An agency is less likely to cooperate if it overestimates the number of clients it expects to lose or underestimates the number of new clients it expects to gain. Even if agencies are correct on average in their estimates of [Pi](j) and [Beta](l; j). misestimated components make cooperation less likely. Estimation could be difficult if anarcho-capitalism has been in a no exit equilibrium.

Second, the coalition may act aggressively toward nonmember agencies. As the number of agencies in C increases, the benefit to C of confronting an independent agency (A) and the probability C wins increase. In the limit the situation resembles that between an individual and a protection agency. If C is sufficiently large it could intimidate A into allowing its disgruntled clients to exit. The coalition attains the benefits of cooperation with A without having to allow its unhappy clients to join A.

V. Evidence and Implications

The arguments presented in the previous section suggest the relationship between private protection agencies and individuals may not be as one-sided as the distribution of power. Empirical evidence is necessary to decide the issue. The model of anarcho-capitalism is abstract and speculative and since it has never been explicitly implemented, no direct test exists. Several social situations, however, resemble the model fairly closely and the nature of asymmetric power relations in these cases provide some evidence concerning the effectiveness of devices discussed in IV.

Competition between local governments within a federal system is one example, although the analogy is not exact. The efficient equilibria of Tiebout models of local public goods provision illustrate the potential for competition when the costs of movement are low. Cities and states do offer different sets of laws in the form of zoning ordinances, traffic laws, and community standards. San Francisco, New Orleans, and Provo, Utah, are clearly catering to different groups of citizens. States compete with one another for businesses, both in general laws (on incorporation and collective bargaining) and with specific tax concessions and subsidies as with the Saturn Corporation and professional sports teams. Competition between local governments within a federal system differs from anarcho-capitalism in one important respect: the national government prohibits the local governments from interfering with citizen mobility.(10)

International migrations affect national policies. But nations can impose restrictions on the movement of persons, capital, and wealth instead of modifying their policies. Hence competition between national governments is a very close approximation of anarcho-capitalism. The German Democratic Republic was extremely susceptible to its citizens voting with their feet throughout its entire existence. Over two and a half million people fled to West Germany between 1949 and 1961, prompting the erection of the Berlin Wall [23, 5]. Migration, first in the tens of thousands through Hungary in the summer of 1989 and then in the millions following the collapse of the Wall in November, brought about reunification. The Iron Curtain shows, however, that nations can effectively restrict the movements of their citizens. International capital and wealth flows can also constrain governments and recent developments in communications, information-transmission, and travel have significantly reduced the effectiveness of governmental restrictions on mobility [24]. And restrictions on mobility impose a cost on national governments in foregone foreign investment and technology which may outweigh the benefits of a captive population. Competitive pressures may force a nation to accept liberalization [11].

In addition to placing restrictions on their own citizens, nations can also offer inducements for defection, which in part offset the negative controls on mobility of the home country. Higher salaries and better research facilities in the United States were a cause of the "brain drain" emigration of scientists, doctors, and engineers in the 1950s and 1960s. Competition between governments for scholars has a lengthy history, which reveals considerable mobility by and consequently a high standard of living for scholars. The Ptolomies of Egypt lured many scholars from Athens to the Library and Museum of Alexandria [8, 13-16]. Scholars and students at the University of Bologna in the 12th, 13th, and 14th centuries were often targets of raids by other cities in Europe anxious to establish a university [8, 22-27]. One particular group was the object of competing offers from Florence, Sienna, and Padua, and overall more than twenty such migrations occurred. In an effort to prevent such departures, authorities in Bologna first required professors to take an oath not to leave the university and later imposed the death penalty on professors who left without permission. The penalties were less than effective, but the university continued to flourish anyway

... not so much because of the threat of the death penalty ... but because it managed to develop a policy of strengthening the institutional framework of the university and its relations with the authorities of the republic. It also took care that the salaries of the teaching doctors did not lag behind those of other universities [8, 27].

In addition, freedom of movement has alleviated conditions for serfs in the early middle ages [35], for freed slaves in the postbellum South [13], and for prostitutes in the United States [34].

The prostitution market approximates anarcho-capitalism. The relationship between pimps and prostitutes is asymmetric. Theoretically pimps could have to compete with one another for the services of women. Although there is some variance, the relationship often resembles the Protection Racket Exit Game:

The dangers of strolling someone else's tuff are particularly acute for newcomers or "outlaws," those who refuse to work for a pimp. In Boston's famous "Combat Zone" an unwritten code declares that all prostitutes must have pimps. Pimps or their women beat those who try to beat the system [34, 177].

A prostitute who wishes to switch pimps, or to work without a pimp or to retire will find that her current pimp will probably feel quite possessive. Pimps generally wish to control decisions about when a prostitute may leave his group, so that those who leave on their own instigation may find the consequences are severe.... Pimps often inflict violence on unruly prostitutes, as an example to others contemplating rebellion [27, 21].

Freedom of choice between pimps may be wholly absent thwarting possibilities for competition and leading to a distribution of rights which is as lopsided as the distribution of force.

Another example is the asymmetric relationship between bookies and organized crime in the illegal gambling market. The distribution of property is skewed in favor of organized crime which successfully extorts bookies [29, 158-94]. Because they are engaged in illegal activities, the bookies' possessions are not secured by the state. To remain in business, potential customers must be able to locate them, which means the crime syndicate can also always locate and confront the bookmaker. And the syndicate can cheaply "win" a confrontation by use of force or by threatening to reveal the illicit activities to the state authorities. The skewed outcome of the Protection Racket Game is observed.

Bribes to high level officials, soldiers, and police are a way of life in many authoritarian nations. These illustrate that Coasian sidepayments can mitigate the exploitation individuals face. Prostitutes sometimes purchase their freedom from pimps in this fashion [27, 21-22]. A problem with such payments is that they are not legally binding agreements. As a result they are most likely to be effective when the agency cannot renege on its bargain. For example, pimps cannot (legally) coerce women into (or to return to) prostitution. Border guards cannot effectively renege ex post on a deal to let someone slip out of the country.

The rights of local governments within a federal system are not subject to government protection. The rarity of succession indicates many federal republics are in the no exit equilibrium. The historical trend toward stronger national government is a natural result. Swiss cantons, however, have retained a great deal of autonomy. The mountainous terrain of the country provides the cantons tremendous natural defensive advantages securing their initial independence and maintaining an effective exit option.(11) The rights of individuals are also subject to encroachment by government as the erosion of economic liberties under the contract and takings clauses of the U.S. Constitution illustrates [9; 31].

The experience of miners' camps during the California Gold Rush raises the possibility that force asymmetries may not be very great [36]. Coalitions of miners or protection agencies can be defined in terms of transactions costs: these costs must be lower between members of an agency than between members and nonmembers. High transactions costs apparently inhibited the formation of miners' coalitions [36, 47-48]. The persistence of organized crime indicates, however, the mining experience may be atypical. Returns to scale in the conflict technology also influence the development of protection agencies. Organizations of sufficient size to exploit individuals were maintained throughout the Lebanese Civil War of 1975-1990 [14].

What are the prospects for cooperation in anarcho-capitalism? Spontaneous forces must provide secure property rights and enforceable contracts to escape the Hobbesian war of all-against-all. Existing research indicates the latter task can likely be solved contingent on a solution to the former. And some distribution of stable property rights is likely to emerge. What is critical, given the libertarian views of its advocates, is the distribution of rights among individuals and protection agencies. Government and anarcho-capitalism are alternative means of protecting individual rights. I have examined several ways in which the distribution of rights in anarchy might be more equal than the distribution of force between individuals and agencies. Further research is necessary to determine the efficacy of each means. The research would have applications to the situations discussed in this section where stable possessions must emerge. The political rights of ethnic minorities and the sovereignty of small nations are two areas where a more equal distribution of rights than might is desirable on normative grounds.

1. For an examination of reciprocity and reputation in general situations, see Axelrod [1], Benson [3], Kronman [21], and Oye [26]. The role of market forces within the context of a government sponsored market order is examined in Klein and Leffler [18] and Williamson [38].

2. The weaker party often does better than expected in conflict situations due to an incentive to fight harder [15].

3. For elaboration on how such a system might work, see Benson [3,349-78], Friedman [10, 109-64], and Rothbard [28, 219-54]. I most closely follow Friedman. A discussion of the moral aspects of private protection agencies and the minial state is contained in Nozick [25]. "Anarchy" actually successfully governs many informal relations within society [4]. For a bibliography of the literature on anarcho-capitalism, see Benson [3] and Cowen [7].

4. Many of these issues become moot if the protection agencies turn out to be gangs.

5. I assume the distribution of these profits does not affect the choices of any clients in the model.

6. I do not require firms to make positive profit. If firms make zero profit due to fixed costs then v would be the amount by which the typical client's payment exceeds avenge variable costs.

7. For a general discussion of reputation, incentives, and competition see Shapiro and Stiglitz [30].

8. My main concern is agency-individual relations and not the agency-agency contest success function. For a detailed discussion of conflict functions and how they affect equilibrium see [16; 32].

9. The game tree of Figure 2 is a possible representation of this situation; it is not the only plausible representation. In particular the order of play for A and B could be reversed or made simultaneous. As a consequence, I do not use subgame perfect equilibrium since then the analysis would depend on the order of play by A and B.

10. Greater restrictions are placed upon the mobility of firms, such as layoff notices, environmental regulations, required repayment of tax breaks, moral suasion, and litigation to prevent relocation.

11. A viable exit option is crucial in the maintenance of a constitutional contract [22].

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