Interval-Valued Bimatrix Game Method for Engineering Project Management

The bimatrix game theory is concerned with how two players make decisions when they are faced with known exact payoffs. The aim of this paper is to develop a simple and an effective bilinear programming method for solving bimatrix games in which the payoffs are represented by intervals. Because the payoffs of the bimatrix game are intervals, the values of the bimatrix game for both players are intervals as well from the viewpoint of logic. Based on the definition of the values of the bimatrix game for players, the game values may be regarded as functions of payoffs belonging to the payoff intervals, which are proven to be monotonic non-decreasing. A pair of auxiliary bilinear programming models is formulated to obtain the upper bound and the lower bound of the interval-type values of the interval-valued bimatrix game by using the upper bounds and the lower bounds of the payoff intervals, respectively. A real example of the engineering project management problem is used to illustrate the applicability and effectivity of the proposed models and method. Interval-Valued Bimatrix Game Method for Engineering Project Management