ABSTRACT

We consider an extension of a non-cooperative game problem where players have joint binding constraints. In this case, justification of a generalized equilibrium point needs a reasonable mechanism for attaining this state. We combine a penalty method and shares allocation of right-hand sides, which replaces the initial problem with a sequence of the usual Nash equilibrium problems together with an upper level variational inequality as a master problem. In order to obtain a completely decomposable problem at the lower level, we apply its additional equivalent transformation. Convergence of solutions of these auxiliary penalized problems to a solution of the initial game problem is established under weak coercivity conditions.

摘要

我们考虑非合作博弈问题的扩展，其中玩家具有联合约束约束。在这种情况下，广义平衡点的证明需要一个合理的机制来达到这种状态。我们结合了惩罚方法和右手边的份额分配，用一系列常见的纳什均衡问题以及一个上层变分不等式作为主问题代替了初始问题。为了在较低级别获得完全可分解的问题，我们应用其附加的等效变换。在弱矫顽力条件下，这些辅助惩罚问题的解收敛于初始博弈问题的解。