Existence of equilibria in repeated games with long-run payoffs.
Where this comes from
- Record sourced from PubMed, PMID 35259010.
- Also identified by DOI 10.1073/pnas.2105867119 and PMC identifier 8931206.
- Licence recorded as CC BY-NC-ND.
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Abstract
SignificanceNash equilibrium, of central importance in strategic game theory, exists in all finite games. Here we prove that it exists also in all infinitely repeated games, with a finite or countably infinite set of players, in which the payoff function is bounded and measurable and the payoff depends only on what is played in the long run, i.e., not on what is played in any fixed finite number of stages. To this end we combine techniques from stochastic games with techniques from alternating-move games with Borel-measurable payoffs.