SPATIAL GAMES WITH PROBABILISTIC PAYOFF FUNCTION

Spatial games are a special type of evolutionary games in which players are distributed over a lattice and each player has local interactions with its neighbors. In the literature different methods for determining the conquering strategy has been used, mostly calculated based on a payoff function. Strategies in each stage of the game can be updated either synchronously or asynchronously. In all these methods, the payoff of playing against another player is a deterministic value which can be calculated based on the payoff matrix. In this study, we have examined the behavior of spatial games when payoff is not a deterministic value but it is a probabilistic one which depends on the benefit that each player can get in playing with the other players. Thus, every time that two players play with each other there is a probability for each of them to win the game and their payoff depends on the total value of the game.