Abstract: Traditional interval bimatrix game theory is used to study players. strategy selection problems with interval payoff; however, such a theory does not consider players.strategy selection which may be subjected to various constraints. The purpose of this paper is to develop a simple and an effective bilinear programming method to solve the bimatrix game in which players. strategy selection is constrained, and the payoffs are intervals, which is called the interval bimatrix game with constrained strategy. Firstly, the values of players are regarded as functions of the values in the payoff intervals, which are of monotonicity. Therefore, we construct a pair of auxiliary bilinear programming models, which are used to explicitly compute the upper and lower bounds of the interval values of players in any interval bimatrix game by respectively using the lower and upper bounds of the payoff intervals and corresponding optimal strategies. Finally, based on a case of enterprise and government in developing a low-carbon economy in the situation that their strategies are constrained. The effectiveness, advantages, and applicability of the models and methods proposed in this paper are illustrated by comparing these results with those without considering strategic constraints.

Key words: non-cooperative game, strategy constraint, optimization method, fuzzy set, uncertain information