Research on Cooperative Dual Equilibria with Asymmetric Uncertainty Strategy

The two-player cooperative game with the lowest cost from the perspective of the player's opponent's interests is considered. Based on irrational phenomena and strategy uncertainty in the game and under the assumption that the payoff matrix for each player is exactly known and each player's own strategy set cannot be evaluated while the mixed strategy set may be estimated at an asymmetric bounded closed set (a subset of the mixed strategy set) and the opponent's strategies can be included in the mixed strategy set, a cooperative dual game model is introduced in a bimatrix game. Then by means of the robust optimization technique, a cooperative dual equilibria with two players is investigated. Some results are obtained as follows: the problem of minimization of the opponent's cost can be converted to a linear programming (LP) and solving the corresponding cooperative dual equilibria can be expressed as solving a mixed complementarity problem (MCP) with l_1∩∞-norm uncertainty. Finally, a numerical experiment is provided to illustrate the feasibility and validity of the robust cooperative dual equilibria.