
TL;DR
This paper introduces a novel framework for non-cooperative ergodic and thermodynamic games using invariant measures and establishes the existence of Nash equilibria through ergodic optimization and thermodynamic formalism.
Contribution
It defines Nash equilibrium in ergodic and thermodynamic settings, applying fixed point theorems and thermodynamic tools to establish existence results.
Findings
Existence of Nash equilibria in ergodic and thermodynamic game settings.
Two independent methods for proving equilibrium existence: thermodynamic formalism and Kakutani fixed point.
Examples illustrating equilibrium concepts and connections to ergodic transport and cooperative games.
Abstract
Let and be continuous maps defined on compact sets. Let where is -invariant and is -invariant, be pay-off functions for a game (in the usual sense of game theory) between players that have the set of invariant measures for (player 1) and (player 2) as possible strategies. Our goal here is to establish the notion of Nash equilibrium point for the game defined by this pay-offs and strategies. The main tools came from ergodic optimization (as we are optimizing over the set of invariant measures) and thermodynamic formalism (when we add to the integrals above the entropy of measures in order to define a second case to be explored). Both cases are ergodic versions of non-cooperative games. We show the existence of Nash equilibrium points with two…
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