Implementation of genetic algorithms for a spatial IPD game with a generalized objective function

Abstract

We discuss the implementation of genetic algorithms for the evolution of cooperative behavior in a spatial IPD (iterated prisoner's dilemma) game with a generalized objective function. Our IPD game has two characteristic features, which make it different from the standard IPD game. One is its spatial structure. Players are spatially fixed in a two-dimensional grid-world. A player, which is located in a cell of the grid-world, plays the IPD game against only eight players in its neighboring cells (not against all the other players). The other characteristic feature is the use of a generalized objective function for each player, which is defined as a weighted sum of the player's payoff and its opponent's payoff. Each player has its own objective function (i.e. its own weight values). For example, a cooperative player may have a positive weight for its opponent's payoff. On the other hand, a hostile player may have a negative weight for its opponent's payoff. We also examined a new matchmaking scheme in our spatial structure. A player in the new matchmaking scheme plays a one-shot game against one of the neighboring players. That is, the IPD game is taken place just once against one of the neighboring players. The point, which makes it different from the standard one-shot game, is its spatial structure and iterative nature. That is, the one-shot game is iterated by randomly selecting a neighboring player as an opponent at each iteration. From various computer simulations, we show that the evolution of cooperative behavior depends on the spatial structure and the objective function.