{"id":862,"date":"2025-02-17T18:41:01","date_gmt":"2025-02-17T18:41:01","guid":{"rendered":"https:\/\/www.ccor.hu\/?p=862"},"modified":"2025-02-17T18:41:01","modified_gmt":"2025-02-17T18:41:01","slug":"corvinus-game-theory-seminar-35","status":"publish","type":"post","link":"http:\/\/www.ccor.hu\/?p=862","title":{"rendered":"Corvinus Game Theory Seminar"},"content":{"rendered":"\n

Feb. 27 (10:00-11:00) room C.510<\/strong><\/p>\n\n\n\n

Rida Laraki <\/strong><\/strong>(Moroccan Center for Game Theory, UM6P, \u00a0https:\/\/mcgt.um6p.ma<\/a> )<\/p>\n\n\n\n

On the relationship between some strategic properties of Nash equilibria and their fixed point index<\/strong><\/p>\n\n\n\n

This talk will explore the relationship between some strategic stability properties of mixed Nash equilibria and their fixed point index in finite games. Specifically, we will establish the following results:<\/p>\n\n\n\n

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  1. A Nash equilibrium is isolated with an index of +1 if and only if it can be transformed into the unique equilibrium of a larger game by introducing inferior replies. This resolves a conjecture explicitly proposed by Hofbauer (2003) and implicitly suggested by Myerson (1996).<\/li>\n\n\n\n
  2. A Nash component admits an equilibrium with an index of +1 near it for every perturbation of a strategically equivalent game if and only if it has a positive index.<\/li>\n\n\n\n
  3. In any finite game, for any selection of equilibria within Nash components and any assignment of +1\/-1 indices to these equilibria such that their sum equals the index of the corresponding component, there exists a perturbation of a strategically equivalent game whose equilibria are close to the selected ones, preserving the assigned indices.<\/li>\n<\/ol>\n\n\n\n

    References:<\/p>\n\n\n\n