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

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