Designing a Decision Making System for a Market-Selection Game

This paper describes how a decision-making system for a market-selection game can be automatically designed through the iteration of the game. Our market-selection game is a non-cooperative repeated game where many players compete with one another at several markets. At each iteration, each player is supposed to choose a single market for maximizing his own profit by selling his product. It is assumed that the market price of the product is determined by the demand-supply relation in each market. In this manner, the market price at each market is determined by the actions of all players. Each player's profit at each iteration depends on the market price at the selected market. So each player wants to choose a market with a high market price, i.e., a market not chosen by many other players. In this paper, we design a decision-making system that automatically chooses a single market for a player based on the market prices of all markets at the previous iteration of the game. We show two approaches to the design of the decision-making system. In one approach, our task is handled as a pattern classification problem, where a feature vector consists of the market prices at the previous iteration. The class label for that feature vector is the market from which the player would have obtained the highest profit at the previous iteration if he/she had chosen that market. In this manner, a single input-output pair is obtained from each iteration of the game so the available information for the design of the decision-making system increases at each iteration. In this approach, our task can be viewed as an on-line learning of a pattern classification system. Another approach is based on a fuzzy reinforcement learning technique. Here, knowledge related to the market selection is automatically acquired in the form of fuzzy if-then rules through the iteration of the game. The antecedent part of each fuzzy if-then rule is linguistically conditioned by the market prices at the previous iteration. Computer simulations on a market selection game with 100 players and 5 markets show that high profits are obtained by decision-making systems designed by our two approaches. Performance evaluation of each approach is performed by the competition with tailored strategies such as a minimum transportation cost strategy, an optimal strategy for the previous actions, a mimic strategy of the nearest neighbor player, a Q -learning-based strategy, a random selection strategy. The adaptability of each approach to the change of market conditions is also examined by computer simulations where the demand-supply relation of each market and/or the strategies of other players are changed during the repeated execution of the market selection game.