Feb. 27 (10:00-11:00) room C.510
Rida Laraki (Moroccan Center for Game Theory, UM6P, https://mcgt.um6p.ma )
On the relationship between some strategic properties of Nash equilibria and their fixed point index
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:
- 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).
- 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.
- 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.
References:
- S. Govindan, R. Laraki, L. Pahl, On sustainable equilibria, Journal of Economic Theory, Volume 213, 2023
- S. Govindan, R. Laraki, L. Pahl, O’Neill’s Theorem for Games, https://arxiv.org/pdf/2312.03392v2 (under minor revision at Mathematics of Operations Research)
- Hofbauer, J., 2003. Some thoughts on sustainable/learnable equilibria. In: Conference Book of the XV Italian Meeting of Game Theory and Applications. Urbino, IT. Universitá degli Studi di Urbino.
- Myerson, R.B., 1996. Sustainable equilibria in culturally familiar games. In: Albers, W., et al. (Eds.), Understanding Strategic Interaction: Essays in Honor of Reinhard Selten. Springer Verlag, Berlin, pp. 111–121.