A note on Brandl and Brandt’s axiomatic characterization of Nash equilibrium

Schroeder, Andreas (2024): A note on Brandl and Brandt’s axiomatic characterization of Nash equilibrium.

Abstract

The axiomatic requirements in Brandl and Brandt (2024) make it possible to define solution concepts that do not select the set of all Nash equilibria as claimed. More precisely, it is possible to construct solution concepts that fulfill the axiomatic requirements, but in certain games no equilibrium is selected at all, as a simple example shows.

• Item Type: MPRA Paper
• Language: English
• Keywords: Non-coporative Game Theory, Nash Equilinrium, Solution Concept
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

References

Brandl, Florian and Felix Brandt (2024), “An axiomatic characterization of Nash equilibrium” Theoretical Economics 19 (2024), 1473–1504.

Peleg, Bezalel and Stef H. Tijs (1996), “The consistency principle for games in strategic form.” International Journal of Game Theory, 25, 13–34.

Schade, Christian, Andreas Schroeder and Kai Oliver Krause (2010) “Coordination after gains and losses: Is prospect theory’s value function predictive for games?” Journal of Mathematical Psychology 55, 426-445.