The path integral formula for the stochastic evolutionary game dynamics

Although the long-term behavior of stochastic evolutionary game dynamics in finite populations has been fully investigated, its evolutionary characteristics in a limited period of time is still unclear. In order to answer this question, we introduce the formulation of the path integral approach for...

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Bibliographic Details
Published in:Europhysics letters 2023-06, Vol.142 (6), p.62001
Main Authors: Li, Minlan, An, Kun, Liu, Chang, Tao, Yi, Wang, Chao, Wang, Rui-Wu
Format: Article
Language:English
Subjects:
Dynamics
Game theory
Probability theory
Transition probabilities
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Summary:Although the long-term behavior of stochastic evolutionary game dynamics in finite populations has been fully investigated, its evolutionary characteristics in a limited period of time is still unclear. In order to answer this question, we introduce the formulation of the path integral approach for evolutionary game theory. In this framework, the transition probability is the sum of all the evolutionary paths. The path integral formula of the transition probability is expected to be a new mathematical tool to explore the stochastic game evolutionary dynamics. As an example, we derive the transition probability for stochastic evolutionary game dynamics by the path integral in a limited period of time with the updating rule of the Wright-Fisher process.
ISSN:0295-5075
1286-4854
DOI:10.1209/0295-5075/acd9eb