A kernel based learning method for non-stationary two-player repeated games

Repeated games is a branch of game theory, where a game can be played several times by the players involved. In this setting, players may not always play the optimal strategy or they may be willing to engage in collaboration or other types of behavior which might lead to a higher long-term profit. Since the same game is repeated for several rounds, and considering a scenario with complete information, it is possible for a player to analyze its opponent’s behavior in order to find patterns. These patterns can then be used to predict the opponent’s actions. Such a setting, where players have mutual information about past moves and do not always play in equilibrium, leads naturally to non-stationary environments, where the players can frequently modify their strategies in order to get ahead in the game. In this work, we propose a novel algorithm based on a string kernel density estimation, which is capable of predicting the opponent’s actions in repeated games and can be used to optimize the player’s profit over time. The prediction is not limited to the next round action. It can also be used to predict a finite sequence of future rounds, which can be combined with a lookahead search scheme with limited depth. In the experiments section, it is shown that the proposed algorithm is able to learn and adapt rapidly, providing good results even if the opponent also adopts an adaptive strategy.