Survival of dominated strategies under imitation dynamics

TL;DR

This paper investigates how different imitation dynamics influence the survival of strictly dominated strategies in evolutionary game theory, showing that certain protocols can allow these strategies to persist.

Contribution

It introduces and analyzes imitation protocols that can enable dominated strategies to survive, challenging the traditional view of their inevitable extinction.

Findings

Certain imitation protocols favor rare strategies.

Dominated strategies can persist at nontrivial frequencies.

Survival depends on the specific imitation dynamics used.

Abstract

The literature on evolutionary game theory suggests that pure strategies that are strictly dominated by other pure strategies always become extinct under imitative game dynamics, but they can survive under innovative dynamics. As we explain, this is because innovative dynamics favour rare strategies while standard imitative dynamics do not. However, as we also show, there are reasonable imitation protocols that favour rare or frequent strategies, thus allowing strictly dominated strategies to survive in large classes of imitation dynamics. Dominated strategies can persist at nontrivial frequencies even when the level of domination is not small.