Study on forecasting equilibrium of matrix game based on grey information of players' decision rules

Outsiders and players usually behave different information about game, which may have different purposes about the game. This paper develops a novel approach for the above game that players have more than one decision rules and implement them by probabilities which may be interval numbers. So that outsiders can use this approach to forecast the equilibrium of the game, corresponding probability and the payoff if the probability distributions of alternative decision rules are known. In fact, the given approach can be regarded as an extension of the classic strategic form representation of game as it can be used to analyze the game in which players have single decision rule as well.