Evolutionary dynamics in heterogeneous populations: a general framework for an arbitrary type distribution

Dai Zusai ()
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Dai Zusai: Tohoku University

International Journal of Game Theory, 2023, vol. 52, issue 4, No 10, 1215-1260

Abstract: Abstract We present a general framework of evolutionary dynamics under persistent heterogeneity in payoff functions and revision protocols, allowing continuously many types in a game with finitely many strategies. Unlike existing literature, we do not assume anonymity of the game nor aggregability of the dynamic. The dynamic is formulated as a differential equation of a joint probability measure of types and strategies. To establish a foundation for this framework, we clarify regularity assumptions on the revision protocol, the game, and the type distribution to guarantee the existence of a unique solution trajectory as well as those to guarantee the existence of an equilibrium in a heterogeneous population game. We further verify equilibrium stationarity in general and stability in potential games under admissible dynamics. Our framework encompasses a wide range of possible applications, including incomplete information games and spatial evolution.

Keywords: Evolutionary dynamics; Heterogeneity; Continuous space; Potential games (search for similar items in EconPapers)
JEL-codes: C61 C62 C73 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00182-023-00867-y

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