The Prisoner's Dilemma considered
Press release issued: 15 April 2004
A diversity of personality types is of central importance to the evolution of co-operation - according to a paper by researchers at Bristol University published in Nature today.
A diversity of personality types is of central importance to the evolution of co-operation – according to a paper by researchers at Bristol University published in Nature today [15 April 2004].
John McNamara and Zoltan Barta of the Department of Mathematics, and Alasdair Houston of the Department of Biological Sciences, considered a game where the Prisoner’s Dilemma game is repeatedly played.
The Prisoner’s Dilemma is a game between two players that captures the tension between individual and communal benefits. In the game each player can either co-operate (contribute towards a common good) or defect (exploit the other player’s contribution).
Defection is the best response to any action by the opponent. Thus if the opponent’s action is unknown the best action is to defect. This is true for both players, so that in a single play of the game, the game-theoretic solution is for each player to defect. This is despite the fact that if both co-operated they would both do better. Because of these properties, the Prisoner’s Dilemma game has become the standard paradigm for investigating the evolution of co-operation.
The paper’s authors considered a game where the Prisoner’s Dilemma is repeatedly played by two opponents. There is a fixed maximum possible number of rounds, where this maximum is known to both players. After each round, the players proceed to the next round only if both have just co-operated.
A standard argument based on working backwards from the last possible round shows that defection on all rounds is the only game-theoretic outcome. This is because it is best to defect on the last round, and given this, it is best to defect on the last but one round, and so on.
Professor McNamara said: “Investigations of cooperation have usually avoided a fixed number of rounds because the above argument precludes the evolution of cooperation. We consider the evolution of a population in which processes such as mutation maintain a diversity of personality types, where personality is here the tendency to cooperate. The presence of this variation means that high levels of cooperation evolve.“Some other investigators have previously incorporated variability, but our theoretical study focuses on a context in which the results are very striking. Our paper brings out the central importance of maintaining a range of personalities in the population for the evolution of cooperation.”