Axelrod's "The Evolution of Cooperation"

Abstract

* Most economists who have studied the behavior of firms have at one time or another wrestled with such questions as: How is collusion among firms sustained? Why do firms sometimes maintain product quality, when cheating on quality would lower costs? and Why do customers sometimes stick with suppliers who do not offer the lowest price? In general, why do firms and individuals sometimes engage in behavior that is plainly unprofitable from a short-run point of view? How do these behaviors emerge, and what sustains them? To the economist's list of questions about cooperative behavior, Axelrod would add several more drawn from other disciplines: How did cooperation emerge between the fungi and algae that compose lichens, or between fig trees and fig wasps, or between certain small fishes and their potential predators, whose mouths the small fishes clean? How did the Live-and-Let-Live system-a system in which opposing German and Allied battalions in trench warfare avoided shooting seriously at each other between major battles-emerge in World War I? What lessons can be drawn from these examples that might be useful in promoting cooperation and reducing conflict among people and nations? Axelrod's approach to studying these questions is based on an analysis of the famous Prisoners' Dilemma game. In that game, each player has two strategies available, labelled Cooperate and Defect, or C and D for short. The payoffs to the players are summarized in Table 1. The first entry in each pair designates the payoff to the row player and the second the payoff to the column player. The letters used in the payoff table are mnemonics: R designates the reward for cooperation, T the temptation to defect, S the sucker's payoff, and P the punishment for mutual defection. It is assumed that T > R, P > S, and R > P. No matter what move one player makes, the other player does best for himself by defecting. Simple self-interest would lead both players to defect and garner a payoff of P. The dilemma is that the pair would be better off if they could agree to cooperate. It is also assumed that mutual cooperation is better for both players than alternating defection and cooperation, that is, T + S < 2R. The Prisoners' Dilemma game has been widely studied by economists, psychologists, game theorists, and others. From the game theorist's point of view the main facts are: (i) the unique Nash equilibrium of the game involves mutual defection, and (ii) cooperation can be supported as an equilibrium phenomenon if the game is repeated infinitely many times without too much discounting (Rubinstein, 1980), or if the game is repeated finitely many times but the players are uncertain about each other's motivation or strategies (Kreps, Milgrom, Roberts, and Wilson, 1982).