基于仿真的博弈系统优化策略研究

OptimizingStrategy for Game TheorySystem Based on the Convex Optimization Method

以石头剪刀布博弈系统为例,提出一种新的理论方法优化该系统,目的是在不受其他因素影响下最大化玩家获得的收益,这种新方法即凸优化.引入非零和矩阵建立凸优化算法模型,定量地创建了石头剪刀布博弈系统收益方程,这种方法前人鲜有研究.创新地提出了博弈系统最优值的临界方程即鞍点方程,并用强对偶理论证明了该方程的正确性.重点研究凸优化中的Newton算法对石头剪刀布博弈系统进行数据仿真和最大化玩家获得的收益.仿真结果表明,数值结果与理论假设相一致,验证了该方法的可行性和正确性.该研究对于理解博弈系统和应用凸优化具有十分重要的意义.

The convex optimization,which serves as a new optimized method,can be fully applied to the game theory system,aiming at maximizing the payoff of the game systems(for all players).The two person non zero sum matrix was introduced to describe the equivalent of payoff in the hypothetical game theory system for making quantitative analyses and getting maximal payoff of the system.A saddle point equation was created to be the critical equation of the optimal value of the game theory system and Newton’s algorithm was used to simulate the game model.The simulation results show that,the results are consistent with the theoretical hypothesis values.The method was tested and verified to be feasible and accurate.The work is helpful for deeply understanding the game theory system and reasonably applying the convex optimization.