The path integral formula for the stochastic evolutionary game dynamics in the Moran process

TL;DR

This paper introduces a path integral formulation for the Moran process in evolutionary game theory, providing a new mathematical tool to analyze stochastic evolutionary dynamics through transition probabilities as sums over all possible paths.

Contribution

It develops a novel path integral approach for the Moran process, enabling the calculation of transition probabilities in stochastic evolutionary game dynamics.

Findings

Derived the path integral formula for transition probabilities

Provided a new mathematical framework for stochastic evolutionary dynamics

Potential to enhance analysis of complex evolutionary processes

Abstract

The Moran process is one of an basic mathematical structure in the evolutionary game theory. In this work, we introduce the formulation of the path integral approach for evolutionary game theory based on the Moran process. We derive the transition probability by the path integral from the initial state to the final state with updating rule of the Moran process. In this framework, the transition probability is the sum of all the evolutionary paths. The path integral formula of the transition probability maybe expected to be a new mathematical tool to explore the stochastic game evolutionary dynamics.