论文标题
关于可持续平衡
On Sustainable Equilibria
论文作者
论文摘要
遵循Myerson（1996）中提出的想法，Hofbauer（2000）将有限游戏的NASH平衡定义为可持续的，如果它可以使其成为通过删除/添加一部分策略来获得较低答复的游戏获得的独特的NASH平衡。本文证明了有关可持续平衡的两个结果。第一个涉及霍夫鲍尔·梅尔森（Hofbauer-Myerson）关于平衡的可持续性及其指数之间关系的猜想：对于一般的游戏类别，如果其指数为$+1 $，则平衡是可持续的。冯·史内格（Von Schemde）和冯·斯滕格尔（Von Stengel，2008）证明了这一猜想是对bimatrix游戏的猜想。我们表明，所有有限游戏的猜想都是正确的。更确切地说，我们证明，当且仅当在较大的游戏中，通过添加有限的许多策略来获得较大的策略，将其变成较大的游戏时，我们就证明了一个孤立的平衡具有指数+1。我们的第二个结果为所有游戏提供了可持续性的公理扩展，并表明只有具有正索引的NASH组件才能可持续。
Following the ideas laid out in Myerson (1996), Hofbauer (2000) defined a Nash equilibrium of a finite game as sustainable if it can be made the unique Nash equilibrium of a game obtained by deleting/adding a subset of the strategies that are inferior replies to it. This paper proves two results about sustainable equilibria. The first concerns the Hofbauer-Myerson conjecture about the relationship between the sustainability of an equilibrium and its index: for a generic class of games, an equilibrium is sustainable iff its index is $+1$. Von Schemde and von Stengel (2008) proved this conjecture for bimatrix games; we show that the conjecture is true for all finite games. More precisely, we prove that an isolated equilibrium has index +1 if and only if it can be made unique in a larger game obtained by adding finitely many strategies that are inferior replies to that equilibrium. Our second result gives an axiomatic extension of sustainability to all games and shows that only the Nash components with positive index can be sustainable.
