NCSU Differential Equations/Nonlinear Analysis Seminars

Location and Time: SAS 4201, Wednesday 15:00 -16:00

Organizers: Lorena Bociu, Patrick Combettes, Ryan Murray, and Khai T. Nguyen

NEXT TALK

Wednesday, Nov 05, 15:00-16:00, Zoom: Link

Speaker: Rida Laraki, Moroccan Center for Game Theory, UM6P (Rabat, Morocco)
Title: On the Relationship Between Strategic Properties of Nash Equilibria and Their Index
Abstract: This talk investigates the relation between some strategic features of mixed Nash equilibria and their fixed point index in finite games. We present new results that deepen our understanding of how equilibrium structure relates to index theory:

1. A mixed Nash equilibrium x is isolated with index +1 if and only if it can be made the unique equilibrium of a larger game, constructed by adding strategies that are strictly inferior responses to x. This settles an open question posed explicitly by Hofbauer (2003) and implicitly by Myerson (1996).

2. A Nash component admits an equilibrium of index +1 in its neighborhood under every perturbation of any strategically equivalent game if and only if the component itself has a positive index.

3. For any finite game, any selection of equilibria from each Nash component, and any assignment of indices ±1 to these equilibria such that their sum equals the index of the component, there exists a perturbation of a strategically equivalent game whose equilibria approximate the selected ones and preserve the assigned indices.

These results bridge equilibrium refinement, index theory, and robustness to strategic perturbations, offering new insights into the structure and stability of Nash equilibria.

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