Problem
Research questions and friction points this paper is trying to address.
Extending dissipativity theory to infinite strategy sets
Deriving stability conditions for Nash equilibria
Generalizing theory to dynamic payoff models
Evolutionary Games on Infinite Strategy Sets: Convergence to Nash Equilibria via Dissipativity
🤖 AI Summary
This study addresses the stability of Nash equilibria under evolutionary dynamics in population games with strategy sets modeled as infinite-dimensional compact metric spaces. Methodologically, it extends dissipativity theory to infinite-dimensional evolutionary systems on the manifold of probability measures, establishing a general stability analysis framework applicable to arbitrary payoff structures. The approach integrates infinite-dimensional dynamical systems theory, monotone operator theory, and differential geometry of measure manifolds, enabling modular verification of dynamical mechanisms against payoff conditions. Theoretical contributions include: (i) unified derivation of stability criteria for multiple classical dynamics—including Brown–von Neumann–Nash and unbiased pairwise comparison dynamics; (ii) natural incorporation of generalized settings such as dynamic payoffs and monotone games; and (iii) successful application to novel continuous-time war-of-attrition games, demonstrating both the generality and practical applicability of the framework.
📝 Abstract
We consider evolutionary dynamics for population games in which players have a continuum of strategies at their disposal. Models in this setting amount to infinite-dimensional differential equations evolving on the manifold of probability measures. We generalize dissipativity theory for evolutionary games from finite to infinite strategy sets that are compact metric spaces, and derive sufficient conditions for the stability of Nash equilibria under the infinite-dimensional dynamics. The resulting analysis is applicable to a broad class of evolutionary games, and is modular in the sense that the pertinent conditions on the dynamics and the game's payoff structure can be verified independently. By specializing our theory to the class of monotone games, we recover as special cases existing stability results for the Brown-von Neumann-Nash and impartial pairwise comparison dynamics. We also extend our theory to models with dynamic payoffs, further broadening the applicability of our framework. We illustrate our theory using a variety of case studies, including a novel, continuous variant of the war of attrition game.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Extends dissipativity theory to infinite strategy sets
Derives stability conditions for Nash equilibria
Applies theory to monotone and dynamic payoff games
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