Evolution of neighborly relations in a spatial IPD game with cooperative players and hostile players

Abstract

We discuss the evolution of cooperative behavior among neighboring players in a spatial IPD (Iterated Prisoner's Dilemma) game where every player is located in a cell of a two-dimensional grid-world. In our game, a player in a cell plays against players in its neighboring cells. A game strategy of a player is denoted by a bit string, which determines the next action based on a finite history of previous rounds of the IPD game. Genetic operations for generating a new strategy of a player are also performed within its neighborhood. We first compare the evolution of cooperative behavior in the spatial IPD game with that in the standard non-spatial IPD game. Next, we examine the effect of the existence of cooperative (or hostile) players on the evolution of cooperative behavior. For representing such players with high flexibility, we use a generalized fitness function defined as a weighted sum of the player's payoff and its opponent's payoff. The fitness of a player depends on not only its payoff but also its opponent's payoff. Every player has its own weight vector in the generalized fitness function. This means that every player is characterized by its weight vector. Then we consider a more general situation where every player has a different weight vector for each of its neighbors. In this situation, we can examine the evolution of a neighborly relation between every pair of neighboring players. A weight vector of a player for a neighbor is updated based on the result of the IPD game between them. Finally, we examine the spatial IPD game with a different matchmaking scheme where the opponent of a player is randomly selected from its neighbors at every round of the IPD game. In such a spatial IPD game, the next action of a player is determined by its strategy (i.e., bit string) based on a finite history of previous rounds of the IPD game with different opponents.