A belief-based evolutionarily stable strategy

TL;DR

This paper introduces a belief-based evolutionarily stable strategy using Dempster-Shafer evidence theory to better model uncertainty in mixed strategies within evolutionary game theory.

Contribution

It proposes a belief strategy framework that accounts for uncertainty in mixed strategies, extending the classical ESS concept with a more realistic approach.

Findings

Belief strategy reduces to mixed strategy under certain conditions.

Belief-based ESS generalizes classical ESS, capturing uncertainty.

Provides a new tool for modeling agent interactions with uncertainty.

Abstract

As an equilibrium refinement of the Nash equilibrium, evolutionarily stable strategy (ESS) is a key concept in evolutionary game theory and has attracted growing interest. An ESS can be either a pure strategy or a mixed strategy. Even though the randomness is allowed in mixed strategy, the selection probability of pure strategy in a mixed strategy may fluctuate due to the impact of many factors. The fluctuation can lead to more uncertainty. In this paper, such uncertainty involved in mixed strategy has been further taken into consideration: a belief strategy is proposed in terms of Dempster-Shafer evidence theory. Furthermore, based on the proposed belief strategy, a belief-based ESS has been developed. The belief strategy and belief-based ESS can reduce to the mixed strategy and mixed ESS, which provide more realistic and powerful tools to describe interactions among agents.