A game-theoretic interpretation of Marcel Mauss' 'The Gift.'

INTRODUCTION

Economists have been increasingly focusing their research efforts on an analysis of power, and the interplay between conflict and cooperation, (Bartlett, 1989).(1) 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 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.(3) 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 [U.sup.A](X,Y), and [U.sup.B](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, "x" 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 [Delta] represent this cost for A; let [Epsilon] 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 [Alpha] represent the amount of good X A …