Game Dynamics and Nash Equilibria

TL;DR

This paper examines the relationship between Nash equilibria and dynamic processes like replicator and best-reply dynamics, highlighting cases where equilibria are eliminated despite their uniqueness.

Contribution

It provides insights into the stability of Nash equilibria under dynamic processes, emphasizing potential discrepancies between equilibrium existence and dynamic elimination.

Findings

Unique Nash equilibria can be eliminated by dynamics from almost all initial conditions

Replicator and best-reply dynamics may not always converge to the equilibrium

The paper discusses conditions under which equilibria are stable or eliminated

Abstract

If a game has a unique Nash equilibrium, then this equilibrium is arguably the solution of the game from the refinement's literature point of view. However, it might be that for almost all initial conditions, all strategies in the support of this equilibrium are eliminated by the replicator dynamics and the best-reply dynamics.