A minimal model for the evolution of cooperation through evolving heterogeneous games

Instituto de Física, Facultad de Ciencias, Universidad de la República - Iguá 4225, 11400 Montevideo, Uruguay

Received: 19 October 2007
Accepted: 18 December 2007

Abstract

How did cooperative behavior evolve is a big open question in both biology as well as in social sciences. This problem is frequently addressed through the evolutionary game theory. However, very often it is not obvious which game is the more appropriate to use. Furthermore, an empirical determination of the payoffs can be very difficult while variations in the payoff values can dramatically alter theoretical predictions. Here, to overcome the above difficulties, I propose a very minimal model without payoff parameters. Instead, starting with random heterogeneous distributions of payoffs, by the process of natural selection itself, definite payoff matrices are produced. The system evolves from a completely heterogeneous distribution of payoffs to a situation in which very few payoff matrices coexist. When the initial set of games consists of dilemma games, the emerging game is the “Stag Hunt”. The fraction of cooperator agents converges in all the cases examined to non-zero values.