多组对策系统非劣Nash策略的功效系数算法

引进多组对策系统组内部合作对策非劣解的线性型功效系数方法,证明最优解是组内部隐含某一权重向量的合作对策的非劣解,由此得到合作对策的单目标规划问题.在组内部该问题的解不仅是非劣的,而且对于所有局中人都优于不合作时的Nash平衡策略.利用组与组之间的非劣反应集,构造求解非劣Nash策略的迭代算法.该算法在保留文献3]优点的前提下,克服其缺点,得到的解优于文献3]对应的解.最后,用实例验证了该算法的有效性和正确性,所得结论丰富了多组对策问题的内容.

Efficiency Coefficient Algorithm for Non-inferior Nash Strategy in Multi -team Game Systems

The algorithm called linear efficiency coefficient for cooperative games within each team in multi-team game systems is introduced to prove that the optimal solution is a non-inferior solution for cooperative game which implies a certain weight vector within each team. By this result, a single objective parameter programming for the cooperative games within each team is developed. The solution of this programming is not only a non-inferior solution but also a strategy superior to Nash equilibrium strategies for all the players within each team. An iterative algorithm for solving non-inferior Nash strategies between the teams is proposed using the non-inferior reaction sets of the teams. The algorithm contains the advantages from literature \3\], and simultaneously overcomes its disadvantages. The solution derived from this algorithm is superior to that from literature \3\]. Finally, an example is taken to verify the effectiveness and the correctness of the algorithm, and the results obtained in the paper will enrich the multi-team game theory.