- Email: [email protected]
A game-theoretic interpretation of Marcel Mauss' ‘The gift’
A Game-Theoretic Interpretation Marcel Mauss’ ‘The Gift’
ROBERT RIDER* California State University,
of
San Marcos
This article proposes that a game theoretic interpretation can be made of Marcel Mauss’ The Gifr. The results provide support for the claim that the institution of reciprocity is a socially stabilizing exchange mechanism. Suppose that the first interactions among different prehistoric tribes or bands were characterized, in the words of Hobbes, as being “short, nasty, and brutish.” In the absence of voluntary exchange institutions, such as reciprocity, through which these groups could interact in more cooperative ways, their initial external interactions may have been characterized by plunder, pillage and war. It is from these conflictive relations that more cooperative institutions may have been chosen or have evolved. This paper shows how the gift, and reciprocity in general, could have allowed for the evolution of more cooperative relations through credible threats of returning to conflict if the gift was not returned. It is argued that the original motivation for the return of the gift may have been to elicit cooperation. Only after this cooperation had been attained could the gift then evolve into the social norm that Mauss had observed. It further suggests that reciprocity may have an origin of conflict.
INTRODUCTION Economists have been increasingly focusing their research efforts on an analysis of power, and the interplay between conflict and cooperation, (Bartlett, 1989).’ The interaction between conflict and cooperation has proven to be highly complex. They are not mutually exclusive. It is best to think of them in their purest forms as lying at opposite *Direct all correspondence to: Robert Rider, Economics Program, California State University, California 92096-0001. Telephone: (760) 750-4140. E-mail: [email protected] The Social Science Journal, Volume 35, Number 2, pages 203-212. Copyright 0 1998 by JAI Press Inc. All rights of reproduction in any form reserved. ISSN: 0362-3319.
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ends of a double continuum. Between these polar ends, though, there are complex mixtures of cooperation and conflict. Social institutions, such as property rights and exchange, can be interpreted as combinations of cooperation and conflict. Even institutions which appear to be of a purely voluntary nature may be supported by or have origins in conflict. By expanding our focus to be inclusive of conflict and power, we have gained important and surprising insights into a myriad of social phenomena.2 This research note proposes a game theoretic interpretation of Marcel Mauss’ The Gift.” The results provide support for the claim that the institution of reciprocity is a socially stabilizing exchange mechanism. Suppose that the first interactions among different prehistoric tribes or bands were characterized, in the words of Hobbes, as being “short, nasty, and brutish.” In the absence of voluntary exchange institutions, such as reciprocity, through which these groups could interact in more cooperative ways, their initial external interactions may have been characterized by plunder, pillage and war. It is from these conflictive relations that more cooperative institutions may have been chosen or have evolved. This paper shows how the gift could have allowed for the evolution of more cooperative relations through credible threats of returning to conflict if the gift was not returned. The original motivation for the return of the gift may have been to elicit cooperation. I will first describe a simple game that models the Hobbesian state of nature. Conditions supporting an equilibrium of mutual predation are discussed. Second, through the derivation of a trigger strategy equilibrium, an escape from this world of mutual predation becomes possible. It is shown that cooperation is more easily sustained the greater are the production and defensive skills, and the smaller are the predation skills of both players. Finally, these results are used to develop a game theoretic interpretation of Mauss’ work and the general concept of reciprocity. In particular, the system of total prestations and the social obligations attached to this institution closely correspond to the trigger strategies which initiate and sustain cooperation.
THE
GAME
Let there be two clans, or players, A and B. Each produces a particular good with its labor endowment. A produces Y, and B produces X. Each has a utility function defined over both goods. (Superscripts will denote the player.) Let UA(X, y), and @(X, Y) be the utility functions for A and B respectively. The standard assumptions will be made.4 If A uses all of its labor to produce Y, then “y” is the total amount it can produce. Similarly for B, “2 is the total amount of good X it can produce. Since this is the Hobbesian state of nature, a world without law, a time when there is “war of every man against every man,” the activity of predation (stealing and pillaging) is also available to each of the players. But predation is costly. It requires labor, which will reduce the amount of production during any period of time. It may also entail a loss of life or injury as the other clan defends itself. Let 3 represent this cost for A; let E represent this cost for B. Predation, though, does have its benefits. Each predator is able to steal some of the other player’s production. Let a represent the amount of good X A is able to steal from B; let p represent the amount of good Y B is able to steal from A.
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We now have the following bimatrix game5 (See the state of nature game below.) If both players choose not to prey upon one another, each only consumes the good they each produce. Their payoffs are: UA(O,y) and UB(x,O). This is auk&y. If A preys but B does not, then A’s payoff is uA(a,y-&. B’s payoff is @(x-a,O). This is something akin to a lordship relationship, where A extracts tribute from B. A would be “lord’ over B. By symmetry, if B preys on A but A only produces, their payoffs are: VA(O,y-p) and VE (X-E, p) . Here B is lord overA. If both players produce and prey on one another, then the payoffs are the following. A’s payoff is U*(a,y-3-P); while B’s payoff is UB(x-&-a$). This is a mutual predatory state, or mutual predation.
State of Nature Game B No Predation
Predation
No
Predation A Predation
Suppose that the following relationships hold,
and
r/B(x-E$,> c&O) uE(x-&-a,p> > UE(x-c&o>. Mutual predation describes the equilibrium that would prevail in the Hobbesian state of nature. The above assumptions ensure that mutual predation is the dominant strategy Nash equilibrium.
ESCAPING FROM MUTUAL PREDATION I will now allow this game to be infinitely repeated. Let t denote time. Let each player discount the future by the discount factor 8’. @‘=ll(l+r)‘, where r is the player’s discount rate.) Given that these two players are interacting in this mutually predatory state, where life is “short, nasty and brutish,” is there an escape? Is there a way out which will still allow them to interact, to exchange their different goods? Can a more benign exchange
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process emerge from this hostile and wasteful equilibrium? Can all of this be achieved without the Leviathan? We might expect that these two players eventually would strive for a relationship that preserved the distribution of goods established by this predatory exchange but at a lower cost. They might not communicate explicitly for fear of being left vulnerable. One or both players might have reasoned as follows: Since historically our interactions have led to certain amounts of our products being stolen at great cost, why not end the predation, thus saving the loss of life and limb, and reallocate that labor to production. To appease my adversary, I will make available to him the amount of my good that he normally steals (the gift). I will expect him to reciprocate, though. If not, I will again prey on him and return to mutual plunder. This reasoning can be modeled as the following trigger strategy.6 t=O: Cooperate and only produce, offer the other player the amount he normally stole. DO: Cooperate and only produce, offer the other player the amount he normally stole ONLY IF for all r < t he also cooperated, only produced and reciprocated by offering an amount of his good that I normally stole; otherwise, prey on him. Proposition Mutual cooperation (zero predation) plus exchange is supported as a subgame perfect Nash equilibrium if
and
UB(.),cF(x,a-p,- c&X$- p, Cry.) d&E - a$, - UB(x- E$) (The proof is in the appendix)
The familiar interpretation of this result is that if both players place sufficient weight on future interactions, if they weigh the future sufficiently large, then cooperation is sustainable. Clearly, the denominators of these two conditions are negative. Therefore, any 8 > 0 will suffice if 3 > l3 and E > a. This is intuitively obvious. If the amount of the good
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each player offers to the other is less than his own loss from predation, then clearly he is better off by making the offer no matter how much he weighs the future. Even if this does not hold, there may still be values of 8 which allow for mutual cooperation plus exchange to emerge as the equilibrium in the infinitely repeated game. There is a way out of the Hobbesian state of nature. In fact, it is possible that even if only one of the players places a sufficiently large weight on the future, cooperation may still be possible if sufficient compensation can be made by that player. This compensation, though, would have to be in excess of the predatory amount. A necessary condition for the proposition to hold is that the costs of predation be positive (a, E > 0). The Hobbesian state of nature must be costly, in the sense of lost production, so that the players will have an incentive to choose cooperation. The larger are these costs, the lower is the minimum value for 8 that supports cooperation. These costs are larger the more productive the player; the more productive that a player is, the more production that is lost when labor is allocated to predation. This suggests that there is a minimum level of productivity sufficient for cooperation to be sustainable. In contrast, the more skilled the predator, the larger is the minimum value for 8 supporting cooperation. The greater the predatory skill, the greater is the benefit for remaining in the Hobbesian world of every man for himself. This skill, though, is negatively affected by the defensive skill of the other player. Therefore, the greater is the defensive skill of the other player, the lower is the bound supporting cooperation. A player confronting a strong predator, can induce the predator to consider cooperating by expanding his defense. In sum, cooperation is more easily sustained the greater are the reduction and defensive skills, and the lower are the predation skills of both players. P
AN INTERPRETATION OF THE GIFT This result provides an interesting perspective on Marcel Mauss’ study of reciprocal exchange mechanisms, the system of “total prestations.” Mauss was particularly interested when these took the form “ . . .of the gift generously offered.” These “exchanges,” although seemingly “voluntary, disinterested and spontaneous,” were in fact obligatory. As Mauss argued, “. . . although the prestations and counter-prestations take place under a voluntary guise they are in essence strictly obligatory, and their sanction is private or open wa&~rP.~ (Emphasis added.) They imposed obligations on the recipient, not only to receive the gift, but also to reciprocate. One of the purposes of the gift, perhaps its original purpose, may have been to escape from the state of mutual predation. And it was the credible threat of returning to that state which enforced cooperation. This is the reason for the implicit obligation on the part of the recipient to reciprocate. “To refuse to give, or to fail to invite, is - like refusing to accept-the equivalent of a declaration of war.. . .“.9 Note how violence and the threat of violence is intertwined with that of cooperation. They are not mutually exclusive. Violence enforces cooperation. Marshall Sahlins argued that there are parallels between Hobbes and Mauss.” “Thus the close correspondence between the two philosophers: including, if not exactly the gift, at least a similar appreciation of reciprocity as the primitive mode of
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peace...“.” There is a fundamental difference though. Whereas for Hobbes, individuals needed to create a Leviathan, an institution standing over and above them, to enforce cooperation; Mauss, and the analysis presented here, argue that self-enforcing mechanisms can be instituted to ensure cooperation. Furthermore, note that there is no need for a “norm of reciprocity”12 to initiate cooperation. Gouldner (1960) suggested that the norm of reciprocity might initiate cooperation among individuals in a Hobbesian world. His argument, though, presupposes that the norm has already been accepted as a principle to govern relationships. This begs the question of how the norm itself was discovered and adopted as a moral principle. The analysis here suggests that the norm may have developed u&r cooperation was established. Only after individuals had experienced the cooperation made possible by the reciprocity of gift-giving could a norm of reciprocity have developed. It suggests that reciprocity may have an origin which was not peaceful and benign, but rather one best characterized by piracy and pillage. The first gifts would have emerged from power relationships; they would have evolved after a period of mutual predation. The gifts which facilitated the emergence of cooperation and exchange would have been based on those claims which were established during this earlier mutual predatory period. These predatory claims may have then defined the initial set of moral obligations for the first manifestation of the norm of reciprocity. These gifts would have reflected the predatory skills of the players. The more skilled the predator, the larger the gift that the predator would have been able to secure from his opponent in order to establish cooperation. In time, these gifts may have become institutionalized as a form of reciprocal exchange, yet may have retained some of the vestiges of this earlier period of predation. ’ 3 Mauss observed that the gift was a “total social phenomenon,” “. . .at once legal, economic, religious, aesthetic, morphological and so on”. I4 These societies often distinguished it from “straightforward exchange.” The game presented here reduces a very complex social phenomenon to a single dimension which is primarily economic in nature; in particular, it does not capture the “spirit of the gift,” what the Maori called hau . In fact, it is this inalienability of person and thing which Mauss argued was the motivation behind the obligation of returning the gift. It is argued here, though, that, at least originally, the motivation was to avoid a return to conflict. The role of the first gifts was to resolve conflict, and allow for the development of more cooperative relations. Once established, social norms and customs, these other dimensions of the gift that Mauss observed, may have evolved, reinforcing the institution of reciprocity. This socialization and ritualization of the gift could be incorporated in the game as an evolution of the payoffs of the game over time such that each player’s net payoff of deviating from the norm would be reduced, making any departure from cooperation “less likely.” The benefit from practicing the social norm would increase the “psychic benefit” associated with the reciprocity strategy, and the cost of of violating this same social norm would increase the “psychic cost” of the predation strategy. In light of this explanation, one can think of the game analysis presented here as being more fundamental, that is, at a more primitive level of analysis. The game captures the essence of the original role that the gift may have played, namely, to peacefully resolve conflict. It was in the self-interest of each player to practice gift-
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giving for it would have allowed for the establishment of a preferred social equilibrium. In time, new social values, beliefs and customs may have emerged which would have further enhanced the stabilizing properties associated with the institution of reciprocity’ 5 but this should not obfuscate our understanding of the original purpose of the gift: eliciting and maintaining coo eration. Using Sahlins’ model of reciprocity P6 a plausible story of the evolution of reciprocity emerges. When two prehistoric tribes or bands, each specializing in different divisions of labor, encountered one another, they initially may have established a negative reciprocal relationship. According to Grierson (1980), the “stranger” was disliked with great intensity, and regarded as “scarcely human.” The stranger was seen as without rights. It was not theft to rob a stranger; it was not murder to kill this “enemy” of the tribe. Their initial relationship would have been one of pillage and plunder, if not war. As they continued to engage in this relationship over time, though, a Pareto improvement may have become possible. A more cooperative social equilibrium would reduce the transactions costs from conflict, allowing for resources originally employed in predation to be reallocated to more productive uses. The relationship would have evolved from one which was primarily conflictual to one which was more cooperative; it would have progressed along the cooperation-conflict continuum. It is the gift which may have enabled this social evolution, providing the necessary link between predation and cooperation. Further institutionalization and ritualization of this gift-giving would have only strengthen its cooperation-eliciting properties; but cooperation would continue to be sanctioned by the credible threat of returning to conflict. CONCLUSION Throughout history, exchange and plunder/war often have been mutually entangled in complex ways. As quoted in Sahlins (1972), Levi-Strauss stated “(t)here is a link, a continuity, between hostile relations and the provision of reciprocal prestations. Exchanges are peacefully resolved wars, and wars are the result of unsuccessful transactions.” I have shown through a simple game how reciprocity in the form of giftgiving may have enabled prehistoric peoples to move from relationships based on conflict and predation to ones of a more cooperative nature. The credible threat of returning to conflict inherent in the concept of the gift could have initiated and sustained this cooperation. Although Mauss argued that the set of obligations established by gift-giving arose from the inseparability of thing and person, the spirit of the gift, its original purpose may have been for escaping the Hobbesian world of violence and conflict. APPENDIX Proof of the Proposition: I will first show that mutual cooperation with exchange where both players play their trigger strategies is a Nash equilibrium. Then I will show that it is subgame perfect.
10
THE
Suppose that B plays his trigger strategy, all time. A’s payoff will be
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and player A plays his trigger strategy for
UAWY - 8)
(1)
l-CIA
If A follows his trigger strategy until period 7, on B, his largest payoff will be
and then in period
T chooses to prey
T-l
c BA’UA(a,y-P)+BATUA(a,y-,)+ c eA’UA(a,y-&p), t=
t=O
t+ I
Note that this is the largest payoff to player A since player B is playing his trigger strategy. If (1) is larger than (2), then the trigger strategy for player A is a best reply to the trigger strategy of player B. The first condition in the proposition ensures this. (An analogous argument is used to derive the other sufficient condition in the proposition.) Subgame perfection means that the equilibrium strategy induces an equilibrium on all possible subgames, i.e., on any and all subgames, a player has no incentive to deviate from this equilibrium strategy. Trigger strategies have the peculiar property of partitioning the game into two sets of subgames. The first set is where both players cooperate for t 21 or t=O. For each period in this set player A receives UA(a,y-P), and by the same reasoning as above, playing the trigger strategy induces an equilibrium on this subgame. For the second set of subgames, if A chose to prey in some period T, B in this subgame. will choose to prey for all t > T. This is again an equilibrium (Mutual predation is a one shot Nash equilibrium.) (Analogous reasoning leads to the same conclusion if B chose to prey.) Therefore, the equilibrium is subgame perfect.
NOTES 1.
2.
3. 4.
5. 6. 7.
8. 9.
See, for example, Bartlett (1989) Grossman (1991), Hirshleifer (1988), Skaperdas (1992), and Tullock (1974). Hirshleifer (1994). Simmel (1955) argued early on that there was a social significance for conflict. “ . . .so society, too, in order to attain a determinate shape, needs some quantitative ratio of harmony and disharmony,. . .” Mauss (1967). I assume that each player’s utility function is increasing in the consumption of each good, but increasing at a diminishing rate, i.e. Ut, U2 > 0; U, t, Uz2 -C 0 (where subscripts denote partial derivatives). For a more general form of this game. what I call the Property Rights Game, see Rider (1993). Friedman, 1986, pp. 86-104. There is a complication. The more productive is a player, the more that can be stolen for any given predatory effort. Thus, this will make it more difficult to sustain cooperation. I ignore that complication here. Mauss, 1967, p. 3. Mauss, 1967, p. 11.
A Came-theoretic
10. 11. 12.
13.
14. 1.5.
16.
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Interpretation
Sahlins (1972). Sahlins, 1972, p.178. Reciprocity as purely an exchange mechanism differs from the norm of reciprocity. Following Gouldner (1960). reciprocity as exchange can be conceptualized as “. the pattern of exchange through which the mutual dependence of people, brought about by the division of labor, is realized,” “ . . .a mutually gratifying pattern of exchanging goods and services” based on a general set of obligations. (Gouldner, 1960, pp. 169-70). The norm of reciprocity is the moral dimension of a principle of reciprocity. It determines what the general set of obligations for repayment of benefits should be. This more narrow and morally correct set of obligations is based on the history of previous interaction. Studies of the potlatch of the Kwakiutl Indians of the Pacific northwest reveal a complex intertwining of conflict and violence with exchange, what has been characterized as “fighting with property,” Codere (1950). In describing the visits of the Kiriwina people to the Kitava for mortuary ceremonies, Mauss spoke of the “feigned attack,” ~oulawada , Mauss, 1967, p. 27. Anecdotal linguistic evidence also supports this complex mesh. For example, the English word for “barter” originates from “barater,” the French word meaning “to cheat.” Pryor, 1977, p. 12 1. Mauss, 1967, p. 76. This argument also is consistent with the view of marriage rules as fundamentally systems of exchange. If allowance is made for women to be included as part of the gift-giving (perhaps evolving from some earlier period of abducting women), then the stability of cooperation is greatly enhanced by the exchange of women in marriage. Not only is there an exchange of “goods” but there is the development of intertribal kinship relations. “Exchange-and consequently the rule of exogamy which expresses it-has in itself a social value. It provides the means of binding men together, and of superimposing upon the natural links of kinship the henceforth artificial links-artificial in the sense that they are removed from chance encounters of the promiscuity of family life-of alliance by rule.” LeviStrauss, 1969, p. 480. Sahlins, 1972, pp. 185-210.
REFERENCES Bartlett, R. (1989). Economics and Power: An Inquiry into Human Relations and Markets. Cambridge, MA: Cambridge University Press. Codere, H. (1950). Fighting with Property. Seattle, WA: University of Washington Press. Friedman, J. (1986). Game Theory with Applications to Economics. New York: Oxford University Press. Gouldner, A. W. (1960). The Norm of Reciprocity: A Preliminary Statement. American Sociological Review, 25: 161-178. Grierson, P.J. H. (1980). The Silent Trade. Research in Economic Anthropology, 3: 1-74. Grossman, H. I. (1991). A Generalized Equilibrium Model of Insurrections. American Economic Review, 81: 912-921. Hirshleifer, J. (1988). The Analytics of Continuing Conflict. Syntkese, 76:201-233. Hirshleifer, J. (1994). The Dark Side of the Force: Presidential Address, Economic InquiT, 32: l-9. Levi-Strauss, C. (1949). The Elemenraty Structures of Kinship. Eyre & Spottiswoode. Malinowski, B. (1926). Crime and Custom in Savage Society. London: Routledge & Kegan Paul, Ltd. Mauss, M. (1967).Tke Gift: Forms and Functions of Exchange in Archaic Societies. Translated by I. Cunnison. New York: W.W. Norton Co.
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Pryor. F. L. (1977).The Origins of the Economy: A Compurutive Study of Distribution in Primitive and Peasunt Economies New York: Academic Press. Rider, R. (1993). Power, Property, and Markets. Public Choice,75: 149-157. Sahlins, M. (1972). StoneAge Economics New York: Aldine Publishing Co. Simmel, G. (1955). Cor@ict & the Web c~~Group-A~liation.s Translator by: K. H. Wolff and R. Bendix. New York: The Free Press. Skaperdas, S. (1991). Cooperation, Conflict, and Power in the Absence of Property Rights. Americatl Economic Review, 821726739. Tullock, G. (1974).The Social Dilemma: The Economics (8 Wur and Revolution Fairfax, VA: The Center for the Study of Public Choice.
ROBERT RIDER* California State University,
of
San Marcos
This article proposes that a game theoretic interpretation can be made of Marcel Mauss’ The Gifr. The results provide support for the claim that the institution of reciprocity is a socially stabilizing exchange mechanism. Suppose that the first interactions among different prehistoric tribes or bands were characterized, in the words of Hobbes, as being “short, nasty, and brutish.” In the absence of voluntary exchange institutions, such as reciprocity, through which these groups could interact in more cooperative ways, their initial external interactions may have been characterized by plunder, pillage and war. It is from these conflictive relations that more cooperative institutions may have been chosen or have evolved. This paper shows how the gift, and reciprocity in general, could have allowed for the evolution of more cooperative relations through credible threats of returning to conflict if the gift was not returned. It is argued that the original motivation for the return of the gift may have been to elicit cooperation. Only after this cooperation had been attained could the gift then evolve into the social norm that Mauss had observed. It further suggests that reciprocity may have an origin of conflict.
INTRODUCTION Economists have been increasingly focusing their research efforts on an analysis of power, and the interplay between conflict and cooperation, (Bartlett, 1989).’ The interaction between conflict and cooperation has proven to be highly complex. They are not mutually exclusive. It is best to think of them in their purest forms as lying at opposite *Direct all correspondence to: Robert Rider, Economics Program, California State University, California 92096-0001. Telephone: (760) 750-4140. E-mail: [email protected] The Social Science Journal, Volume 35, Number 2, pages 203-212. Copyright 0 1998 by JAI Press Inc. All rights of reproduction in any form reserved. ISSN: 0362-3319.
San Marcos,
204
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JOURNAL
Vol. 35iNo.
211998
ends of a double continuum. Between these polar ends, though, there are complex mixtures of cooperation and conflict. Social institutions, such as property rights and exchange, can be interpreted as combinations of cooperation and conflict. Even institutions which appear to be of a purely voluntary nature may be supported by or have origins in conflict. By expanding our focus to be inclusive of conflict and power, we have gained important and surprising insights into a myriad of social phenomena.2 This research note proposes a game theoretic interpretation of Marcel Mauss’ The Gift.” The results provide support for the claim that the institution of reciprocity is a socially stabilizing exchange mechanism. Suppose that the first interactions among different prehistoric tribes or bands were characterized, in the words of Hobbes, as being “short, nasty, and brutish.” In the absence of voluntary exchange institutions, such as reciprocity, through which these groups could interact in more cooperative ways, their initial external interactions may have been characterized by plunder, pillage and war. It is from these conflictive relations that more cooperative institutions may have been chosen or have evolved. This paper shows how the gift could have allowed for the evolution of more cooperative relations through credible threats of returning to conflict if the gift was not returned. The original motivation for the return of the gift may have been to elicit cooperation. I will first describe a simple game that models the Hobbesian state of nature. Conditions supporting an equilibrium of mutual predation are discussed. Second, through the derivation of a trigger strategy equilibrium, an escape from this world of mutual predation becomes possible. It is shown that cooperation is more easily sustained the greater are the production and defensive skills, and the smaller are the predation skills of both players. Finally, these results are used to develop a game theoretic interpretation of Mauss’ work and the general concept of reciprocity. In particular, the system of total prestations and the social obligations attached to this institution closely correspond to the trigger strategies which initiate and sustain cooperation.
THE
GAME
Let there be two clans, or players, A and B. Each produces a particular good with its labor endowment. A produces Y, and B produces X. Each has a utility function defined over both goods. (Superscripts will denote the player.) Let UA(X, y), and @(X, Y) be the utility functions for A and B respectively. The standard assumptions will be made.4 If A uses all of its labor to produce Y, then “y” is the total amount it can produce. Similarly for B, “2 is the total amount of good X it can produce. Since this is the Hobbesian state of nature, a world without law, a time when there is “war of every man against every man,” the activity of predation (stealing and pillaging) is also available to each of the players. But predation is costly. It requires labor, which will reduce the amount of production during any period of time. It may also entail a loss of life or injury as the other clan defends itself. Let 3 represent this cost for A; let E represent this cost for B. Predation, though, does have its benefits. Each predator is able to steal some of the other player’s production. Let a represent the amount of good X A is able to steal from B; let p represent the amount of good Y B is able to steal from A.
A Came-theoretic
205
interpretation
We now have the following bimatrix game5 (See the state of nature game below.) If both players choose not to prey upon one another, each only consumes the good they each produce. Their payoffs are: UA(O,y) and UB(x,O). This is auk&y. If A preys but B does not, then A’s payoff is uA(a,y-&. B’s payoff is @(x-a,O). This is something akin to a lordship relationship, where A extracts tribute from B. A would be “lord’ over B. By symmetry, if B preys on A but A only produces, their payoffs are: VA(O,y-p) and VE (X-E, p) . Here B is lord overA. If both players produce and prey on one another, then the payoffs are the following. A’s payoff is U*(a,y-3-P); while B’s payoff is UB(x-&-a$). This is a mutual predatory state, or mutual predation.
State of Nature Game B No Predation
Predation
No
Predation A Predation
Suppose that the following relationships hold,
and
r/B(x-E$,> c&O) uE(x-&-a,p> > UE(x-c&o>. Mutual predation describes the equilibrium that would prevail in the Hobbesian state of nature. The above assumptions ensure that mutual predation is the dominant strategy Nash equilibrium.
ESCAPING FROM MUTUAL PREDATION I will now allow this game to be infinitely repeated. Let t denote time. Let each player discount the future by the discount factor 8’. @‘=ll(l+r)‘, where r is the player’s discount rate.) Given that these two players are interacting in this mutually predatory state, where life is “short, nasty and brutish,” is there an escape? Is there a way out which will still allow them to interact, to exchange their different goods? Can a more benign exchange
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process emerge from this hostile and wasteful equilibrium? Can all of this be achieved without the Leviathan? We might expect that these two players eventually would strive for a relationship that preserved the distribution of goods established by this predatory exchange but at a lower cost. They might not communicate explicitly for fear of being left vulnerable. One or both players might have reasoned as follows: Since historically our interactions have led to certain amounts of our products being stolen at great cost, why not end the predation, thus saving the loss of life and limb, and reallocate that labor to production. To appease my adversary, I will make available to him the amount of my good that he normally steals (the gift). I will expect him to reciprocate, though. If not, I will again prey on him and return to mutual plunder. This reasoning can be modeled as the following trigger strategy.6 t=O: Cooperate and only produce, offer the other player the amount he normally stole. DO: Cooperate and only produce, offer the other player the amount he normally stole ONLY IF for all r < t he also cooperated, only produced and reciprocated by offering an amount of his good that I normally stole; otherwise, prey on him. Proposition Mutual cooperation (zero predation) plus exchange is supported as a subgame perfect Nash equilibrium if
and
UB(.),cF(x,a-p,- c&X$- p, Cry.) d&E - a$, - UB(x- E$) (The proof is in the appendix)
The familiar interpretation of this result is that if both players place sufficient weight on future interactions, if they weigh the future sufficiently large, then cooperation is sustainable. Clearly, the denominators of these two conditions are negative. Therefore, any 8 > 0 will suffice if 3 > l3 and E > a. This is intuitively obvious. If the amount of the good
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each player offers to the other is less than his own loss from predation, then clearly he is better off by making the offer no matter how much he weighs the future. Even if this does not hold, there may still be values of 8 which allow for mutual cooperation plus exchange to emerge as the equilibrium in the infinitely repeated game. There is a way out of the Hobbesian state of nature. In fact, it is possible that even if only one of the players places a sufficiently large weight on the future, cooperation may still be possible if sufficient compensation can be made by that player. This compensation, though, would have to be in excess of the predatory amount. A necessary condition for the proposition to hold is that the costs of predation be positive (a, E > 0). The Hobbesian state of nature must be costly, in the sense of lost production, so that the players will have an incentive to choose cooperation. The larger are these costs, the lower is the minimum value for 8 that supports cooperation. These costs are larger the more productive the player; the more productive that a player is, the more production that is lost when labor is allocated to predation. This suggests that there is a minimum level of productivity sufficient for cooperation to be sustainable. In contrast, the more skilled the predator, the larger is the minimum value for 8 supporting cooperation. The greater the predatory skill, the greater is the benefit for remaining in the Hobbesian world of every man for himself. This skill, though, is negatively affected by the defensive skill of the other player. Therefore, the greater is the defensive skill of the other player, the lower is the bound supporting cooperation. A player confronting a strong predator, can induce the predator to consider cooperating by expanding his defense. In sum, cooperation is more easily sustained the greater are the reduction and defensive skills, and the lower are the predation skills of both players. P
AN INTERPRETATION OF THE GIFT This result provides an interesting perspective on Marcel Mauss’ study of reciprocal exchange mechanisms, the system of “total prestations.” Mauss was particularly interested when these took the form “ . . .of the gift generously offered.” These “exchanges,” although seemingly “voluntary, disinterested and spontaneous,” were in fact obligatory. As Mauss argued, “. . . although the prestations and counter-prestations take place under a voluntary guise they are in essence strictly obligatory, and their sanction is private or open wa&~rP.~ (Emphasis added.) They imposed obligations on the recipient, not only to receive the gift, but also to reciprocate. One of the purposes of the gift, perhaps its original purpose, may have been to escape from the state of mutual predation. And it was the credible threat of returning to that state which enforced cooperation. This is the reason for the implicit obligation on the part of the recipient to reciprocate. “To refuse to give, or to fail to invite, is - like refusing to accept-the equivalent of a declaration of war.. . .“.9 Note how violence and the threat of violence is intertwined with that of cooperation. They are not mutually exclusive. Violence enforces cooperation. Marshall Sahlins argued that there are parallels between Hobbes and Mauss.” “Thus the close correspondence between the two philosophers: including, if not exactly the gift, at least a similar appreciation of reciprocity as the primitive mode of
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peace...“.” There is a fundamental difference though. Whereas for Hobbes, individuals needed to create a Leviathan, an institution standing over and above them, to enforce cooperation; Mauss, and the analysis presented here, argue that self-enforcing mechanisms can be instituted to ensure cooperation. Furthermore, note that there is no need for a “norm of reciprocity”12 to initiate cooperation. Gouldner (1960) suggested that the norm of reciprocity might initiate cooperation among individuals in a Hobbesian world. His argument, though, presupposes that the norm has already been accepted as a principle to govern relationships. This begs the question of how the norm itself was discovered and adopted as a moral principle. The analysis here suggests that the norm may have developed u&r cooperation was established. Only after individuals had experienced the cooperation made possible by the reciprocity of gift-giving could a norm of reciprocity have developed. It suggests that reciprocity may have an origin which was not peaceful and benign, but rather one best characterized by piracy and pillage. The first gifts would have emerged from power relationships; they would have evolved after a period of mutual predation. The gifts which facilitated the emergence of cooperation and exchange would have been based on those claims which were established during this earlier mutual predatory period. These predatory claims may have then defined the initial set of moral obligations for the first manifestation of the norm of reciprocity. These gifts would have reflected the predatory skills of the players. The more skilled the predator, the larger the gift that the predator would have been able to secure from his opponent in order to establish cooperation. In time, these gifts may have become institutionalized as a form of reciprocal exchange, yet may have retained some of the vestiges of this earlier period of predation. ’ 3 Mauss observed that the gift was a “total social phenomenon,” “. . .at once legal, economic, religious, aesthetic, morphological and so on”. I4 These societies often distinguished it from “straightforward exchange.” The game presented here reduces a very complex social phenomenon to a single dimension which is primarily economic in nature; in particular, it does not capture the “spirit of the gift,” what the Maori called hau . In fact, it is this inalienability of person and thing which Mauss argued was the motivation behind the obligation of returning the gift. It is argued here, though, that, at least originally, the motivation was to avoid a return to conflict. The role of the first gifts was to resolve conflict, and allow for the development of more cooperative relations. Once established, social norms and customs, these other dimensions of the gift that Mauss observed, may have evolved, reinforcing the institution of reciprocity. This socialization and ritualization of the gift could be incorporated in the game as an evolution of the payoffs of the game over time such that each player’s net payoff of deviating from the norm would be reduced, making any departure from cooperation “less likely.” The benefit from practicing the social norm would increase the “psychic benefit” associated with the reciprocity strategy, and the cost of of violating this same social norm would increase the “psychic cost” of the predation strategy. In light of this explanation, one can think of the game analysis presented here as being more fundamental, that is, at a more primitive level of analysis. The game captures the essence of the original role that the gift may have played, namely, to peacefully resolve conflict. It was in the self-interest of each player to practice gift-
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giving for it would have allowed for the establishment of a preferred social equilibrium. In time, new social values, beliefs and customs may have emerged which would have further enhanced the stabilizing properties associated with the institution of reciprocity’ 5 but this should not obfuscate our understanding of the original purpose of the gift: eliciting and maintaining coo eration. Using Sahlins’ model of reciprocity P6 a plausible story of the evolution of reciprocity emerges. When two prehistoric tribes or bands, each specializing in different divisions of labor, encountered one another, they initially may have established a negative reciprocal relationship. According to Grierson (1980), the “stranger” was disliked with great intensity, and regarded as “scarcely human.” The stranger was seen as without rights. It was not theft to rob a stranger; it was not murder to kill this “enemy” of the tribe. Their initial relationship would have been one of pillage and plunder, if not war. As they continued to engage in this relationship over time, though, a Pareto improvement may have become possible. A more cooperative social equilibrium would reduce the transactions costs from conflict, allowing for resources originally employed in predation to be reallocated to more productive uses. The relationship would have evolved from one which was primarily conflictual to one which was more cooperative; it would have progressed along the cooperation-conflict continuum. It is the gift which may have enabled this social evolution, providing the necessary link between predation and cooperation. Further institutionalization and ritualization of this gift-giving would have only strengthen its cooperation-eliciting properties; but cooperation would continue to be sanctioned by the credible threat of returning to conflict. CONCLUSION Throughout history, exchange and plunder/war often have been mutually entangled in complex ways. As quoted in Sahlins (1972), Levi-Strauss stated “(t)here is a link, a continuity, between hostile relations and the provision of reciprocal prestations. Exchanges are peacefully resolved wars, and wars are the result of unsuccessful transactions.” I have shown through a simple game how reciprocity in the form of giftgiving may have enabled prehistoric peoples to move from relationships based on conflict and predation to ones of a more cooperative nature. The credible threat of returning to conflict inherent in the concept of the gift could have initiated and sustained this cooperation. Although Mauss argued that the set of obligations established by gift-giving arose from the inseparability of thing and person, the spirit of the gift, its original purpose may have been for escaping the Hobbesian world of violence and conflict. APPENDIX Proof of the Proposition: I will first show that mutual cooperation with exchange where both players play their trigger strategies is a Nash equilibrium. Then I will show that it is subgame perfect.
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Suppose that B plays his trigger strategy, all time. A’s payoff will be
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and player A plays his trigger strategy for
UAWY - 8)
(1)
l-CIA
If A follows his trigger strategy until period 7, on B, his largest payoff will be
and then in period
T chooses to prey
T-l
c BA’UA(a,y-P)+BATUA(a,y-,)+ c eA’UA(a,y-&p), t=
t=O
t+ I
Note that this is the largest payoff to player A since player B is playing his trigger strategy. If (1) is larger than (2), then the trigger strategy for player A is a best reply to the trigger strategy of player B. The first condition in the proposition ensures this. (An analogous argument is used to derive the other sufficient condition in the proposition.) Subgame perfection means that the equilibrium strategy induces an equilibrium on all possible subgames, i.e., on any and all subgames, a player has no incentive to deviate from this equilibrium strategy. Trigger strategies have the peculiar property of partitioning the game into two sets of subgames. The first set is where both players cooperate for t 21 or t=O. For each period in this set player A receives UA(a,y-P), and by the same reasoning as above, playing the trigger strategy induces an equilibrium on this subgame. For the second set of subgames, if A chose to prey in some period T, B in this subgame. will choose to prey for all t > T. This is again an equilibrium (Mutual predation is a one shot Nash equilibrium.) (Analogous reasoning leads to the same conclusion if B chose to prey.) Therefore, the equilibrium is subgame perfect.
NOTES 1.
2.
3. 4.
5. 6. 7.
8. 9.
See, for example, Bartlett (1989) Grossman (1991), Hirshleifer (1988), Skaperdas (1992), and Tullock (1974). Hirshleifer (1994). Simmel (1955) argued early on that there was a social significance for conflict. “ . . .so society, too, in order to attain a determinate shape, needs some quantitative ratio of harmony and disharmony,. . .” Mauss (1967). I assume that each player’s utility function is increasing in the consumption of each good, but increasing at a diminishing rate, i.e. Ut, U2 > 0; U, t, Uz2 -C 0 (where subscripts denote partial derivatives). For a more general form of this game. what I call the Property Rights Game, see Rider (1993). Friedman, 1986, pp. 86-104. There is a complication. The more productive is a player, the more that can be stolen for any given predatory effort. Thus, this will make it more difficult to sustain cooperation. I ignore that complication here. Mauss, 1967, p. 3. Mauss, 1967, p. 11.
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10. 11. 12.
13.
14. 1.5.
16.
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Sahlins (1972). Sahlins, 1972, p.178. Reciprocity as purely an exchange mechanism differs from the norm of reciprocity. Following Gouldner (1960). reciprocity as exchange can be conceptualized as “. the pattern of exchange through which the mutual dependence of people, brought about by the division of labor, is realized,” “ . . .a mutually gratifying pattern of exchanging goods and services” based on a general set of obligations. (Gouldner, 1960, pp. 169-70). The norm of reciprocity is the moral dimension of a principle of reciprocity. It determines what the general set of obligations for repayment of benefits should be. This more narrow and morally correct set of obligations is based on the history of previous interaction. Studies of the potlatch of the Kwakiutl Indians of the Pacific northwest reveal a complex intertwining of conflict and violence with exchange, what has been characterized as “fighting with property,” Codere (1950). In describing the visits of the Kiriwina people to the Kitava for mortuary ceremonies, Mauss spoke of the “feigned attack,” ~oulawada , Mauss, 1967, p. 27. Anecdotal linguistic evidence also supports this complex mesh. For example, the English word for “barter” originates from “barater,” the French word meaning “to cheat.” Pryor, 1977, p. 12 1. Mauss, 1967, p. 76. This argument also is consistent with the view of marriage rules as fundamentally systems of exchange. If allowance is made for women to be included as part of the gift-giving (perhaps evolving from some earlier period of abducting women), then the stability of cooperation is greatly enhanced by the exchange of women in marriage. Not only is there an exchange of “goods” but there is the development of intertribal kinship relations. “Exchange-and consequently the rule of exogamy which expresses it-has in itself a social value. It provides the means of binding men together, and of superimposing upon the natural links of kinship the henceforth artificial links-artificial in the sense that they are removed from chance encounters of the promiscuity of family life-of alliance by rule.” LeviStrauss, 1969, p. 480. Sahlins, 1972, pp. 185-210.
REFERENCES Bartlett, R. (1989). Economics and Power: An Inquiry into Human Relations and Markets. Cambridge, MA: Cambridge University Press. Codere, H. (1950). Fighting with Property. Seattle, WA: University of Washington Press. Friedman, J. (1986). Game Theory with Applications to Economics. New York: Oxford University Press. Gouldner, A. W. (1960). The Norm of Reciprocity: A Preliminary Statement. American Sociological Review, 25: 161-178. Grierson, P.J. H. (1980). The Silent Trade. Research in Economic Anthropology, 3: 1-74. Grossman, H. I. (1991). A Generalized Equilibrium Model of Insurrections. American Economic Review, 81: 912-921. Hirshleifer, J. (1988). The Analytics of Continuing Conflict. Syntkese, 76:201-233. Hirshleifer, J. (1994). The Dark Side of the Force: Presidential Address, Economic InquiT, 32: l-9. Levi-Strauss, C. (1949). The Elemenraty Structures of Kinship. Eyre & Spottiswoode. Malinowski, B. (1926). Crime and Custom in Savage Society. London: Routledge & Kegan Paul, Ltd. Mauss, M. (1967).Tke Gift: Forms and Functions of Exchange in Archaic Societies. Translated by I. Cunnison. New York: W.W. Norton Co.
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Pryor. F. L. (1977).The Origins of the Economy: A Compurutive Study of Distribution in Primitive and Peasunt Economies New York: Academic Press. Rider, R. (1993). Power, Property, and Markets. Public Choice,75: 149-157. Sahlins, M. (1972). StoneAge Economics New York: Aldine Publishing Co. Simmel, G. (1955). Cor@ict & the Web c~~Group-A~liation.s Translator by: K. H. Wolff and R. Bendix. New York: The Free Press. Skaperdas, S. (1991). Cooperation, Conflict, and Power in the Absence of Property Rights. Americatl Economic Review, 821726739. Tullock, G. (1974).The Social Dilemma: The Economics (8 Wur and Revolution Fairfax, VA: The Center for the Study of Public Choice.