A Dynamic Programming Implemented 2x2 non-cooperative Game Theory Model for ESS Analysis

TL;DR

This paper introduces a dynamic programming approach to compute payoff matrices in a 2x2 non-cooperative game modeling resource allocation between aggressive and non-aggressive individuals, aiding in ESS analysis.

Contribution

It presents a novel dynamic programming method for calculating payoff matrices in finite resource games with biological populations, enabling detailed ESS analysis.

Findings

Dynamic programming effectively computes payoff matrices.

Different aggressive strategies yield distinct ESS.

Method applied to three numerical examples with consistent results.

Abstract

Game Theory has been frequently applied in biological research since 1970s. While the key idea of Game Theory is Nash Equilibrium, it is critical to understand and figure out the payoff matrix in order to calculate Nash Equilibrium. In this paper we present a dynamic programming implemented method to compute 2x2 non-cooperative finite resource allocation game's payoff matrix. We assume in one population there exists two types of individuals, aggressive and non-aggressive and each individual has equal and finite resource. The strength of individual could be described by a function of resource consumption in discrete development stages. Each individual undergoes logistic growth hence we divide the development into three stages: initialization, quasilinear growth and termination. We first discuss the theoretical frame of how to dynamic programming to calculate payoff matrix then give three numerical examples representing three different types of aggressive individuals and calculate the payoff matrix for each of them respectively. Based on the numerical payoff matrix we further investigate the evolutionary stable strategies (ESS) of the games.