Evolutionary Dynamics May Eliminate All Strategies Used in Correlated Equilibria

TL;DR

This paper demonstrates that various evolutionary dynamics can eliminate all strategies in correlated equilibria across a broad class of games, challenging the stability of such equilibria under dynamic processes.

Contribution

It provides the first example showing that multiple dynamics can eliminate all correlated equilibrium strategies in an open set of games.

Findings

Elimination occurs for best-response, Brown-von Neumann-Nash, and other monotonic dynamics.

Elimination is robust to adding mixed strategies as new pure strategies.

The result applies to an open set of 4x4 games.

Abstract

We show on a 4x4 example that many dynamics may eliminate all strategies used in correlated equilibria, and this for an open set of games. This holds for the best-response dynamics, the Brown-von Neumann-Nash dynamics and any monotonic or weakly sign-preserving dynamics satisfying some standard regularity conditions. For the replicator dynamics and the best-response dynamics, elimination of all strategies used in correlated equilibrium is shown to be robust to the addition of mixed strategies as new pure strategies.