Coevolutionary Ant Algorithms Playing Games

Abstract

In this paper, we use the idea of coevolution in the context of ant algorithms to develop game-playing strategies for the simple games of Nim and Tic-Tac-Toe. Since these games have a rather small set of possible non-.nal distinct states (20 for Nim and 627 for Tic-Tac-Toe), we represent a strategyas a lookup-table, specifying for each situation the suggested move. To generate such a strategy, an ant algorithm operates on a ∣S∣ × ∣M∣ pheromone matrix, with ∣S∣ being the number of possible states, and ∣M∣ being the (maximal) number of possible moves per state. We require that the sum of pheromone values in each row is equal to 1. An ant produces a strategy by moving through all the rows and probabilistically(according to the pheromone values in each row) selecting a move for each state.