论文标题
标量线性状态差异游戏的开环和反馈NASH平衡具有冲动控制
Open-loop and feedback Nash equilibrium in scalar linear-state differential games with impulse control
论文作者
论文摘要
我们考虑了一个两人线性状态差异游戏，其中一个玩家在游戏中不断介入，而另一个玩家则实现了冲动控制。当冲动瞬间是外源的时，我们会在开环和反馈纳什平衡重合的线性差异游戏中获得经典结果。当脉冲瞬间是内源性的时，我们表明该结果不再成立。特别是，两个平衡是不同的。我们表明，冲动水平在两个平衡中都是一个常数。更重要的是，在开环情况下，我们表明，冲动的平衡数量最多是一种，而反馈案例中最多可能有两种冲动。
We consider a two-player linear-state differential game, where one player intervenes continuously in the game, while the other implements an impulse control. When the impulse instants are exogenous, we obtain the classical result in linear-state differential games that open-loop and feedback Nash equilibria coincide. When the impulse instants are endogenous, we show that this result no longer holds. In particular, the two equilibria are different. We show that the impulse level is a constant in both equilibria. More importantly, in the open-loop case, we show that the equilibrium number of impulses is at most one, while there can be at most two impulses in the feedback case.
