Learning fuzzy rules from iterative execution of games

This paper discusses the linguistic knowledge extraction from the iterative execution of a multiplayer non-cooperative repeated game. Linguistic knowledge is automatically extracted in the form of fuzzy if-then rules. Our knowledge extraction is mainly based on the on-line incremental learning of fuzzy rule-based systems. In this sense, our linguistic knowledge extraction is the learning of fuzzy rules. We first briefly describe a market selection game, which is formulated as a non-cooperative repeated game with many players and several alternative actions. We also describe some simple strategies for our market selection game. In our market selection game, the payoff of each player depends on the actions of all players. When a particular action is chosen by many players, those players receive low payoff. High payoff is obtained from actions chosen by only a small number of players. This means that minority players with respect to their actions receive high payoff. Next we show how our market selection game can be handled as a pattern classification problem where a single training pattern is successively generated from every round of our game. A fuzzy rule-based classification system is used as a decision-making system by each player for choosing an action in every round. An on-line incremental learning algorithm is proposed for adjusting the fuzzy rule-based classification system. Then we show how our market selection game can be handled as a function approximation problem. A fuzzy rule-based approximation system is used as a value function for approximating the expected payoff from each action. Finally simulation results show that comprehensible linguistic knowledge is extracted by the learning of fuzzy rule-based systems.