论文标题
动态欧洲卷 - 纳什平衡：非电势案例
Dynamic Cournot-Nash Equilibrium: The Non-Potential Case
论文作者
论文摘要
我们考虑在离散时间内进行大量人口动态游戏，其中玩家以时间不断发展的类型为特征。自然的假设是，玩家的行为无法预料其类型的未来价值。这样的游戏以动态的cournot-nash平衡的名义进行，并首先由Acciaio等人研究，作为Blanchet和Carlier在静态情况下设计的游戏的时间/信息依赖性版本，并在额外的假设中以潜在类型为类型。后者意味着可以将游戏简化为辅助变分问题的解决方案。 在目前的工作中，我们研究了动态的cournot-nash均衡性在其自然普遍性中，即超越了潜在案例。作为第一个结果，我们在适当的假设下得出了平衡的存在和唯一性。其次，我们研究了二次情况下自然固定点迭代方案的收敛性。最后，我们说明了前面提到的最佳清算模型和价格影响的结果，这是一种非电势的游戏。
We consider a large population dynamic game in discrete time where players are characterized by time-evolving types. It is a natural assumption that the players' actions cannot anticipate future values of their types. Such games go under the name of dynamic Cournot-Nash equilibria, and were first studied by Acciaio et al., as a time/information dependent version of the games devised by Blanchet and Carlier for the static situation, under an extra assumption that the game is of potential type. The latter means that the game can be reduced to the resolution of an auxiliary variational problem. In the present work we study dynamic Cournot-Nash equilibria in their natural generality, namely going beyond the potential case. As a first result, we derive existence and uniqueness of equilibria under suitable assumptions. Second, we study the convergence of the natural fixed-point iterations scheme in the quadratic case. Finally we illustrate the previously mentioned results in a toy model of optimal liquidation with price impact, which is a game of non-potential kind.
