Insuperable strategies in two-player and reducible multi-player games

TL;DR

This paper explores how population size influences the likelihood of insuperable strategies in two-player and multi-player games, showing that such strategies often dominate evolutionary outcomes in small populations.

Contribution

It introduces the concept of insuperable strategies, highlighting their significance in evolutionary game dynamics beyond traditional rationality assumptions.

Findings

Insuperable strategies often dominate in small populations.

Population size significantly affects evolutionary game outcomes.

The concept extends to multiplayer games with limited reduction methods.

Abstract

Real populations are seldom found at the Nash equilibrium strategy. The present work focuses on how population size can be a relevant evolutionary force diverting the population from its expected Nash equilibrium. We introduce the concept of insuperable strategy, a strategy that guarantees that no other player can have a larger payoff than the player that adopts it. We show that this concept is different from the rationality assumption frequently used in game theory and that for small populations the insuperable strategy is the most probable evolutionary outcome for any dynamics that equal game payoff and reproductive fitness. We support our ideas with several examples and numerical simulations. We finally discuss how to extend the concept to multiplayer games, introducing, in a limited way, the concept of game reduction.