The Truth Behind the Myth of the Folk Theorem
Joseph Y. Halpern, Rafael Pass, Lior Seeman

TL;DR
This paper demonstrates that computing approximate Nash equilibria in repeated games is feasible in polynomial time under cryptographic assumptions, challenging previous beliefs about its intractability.
Contribution
The paper introduces a polynomial-time algorithm for computing approximate Nash equilibria in repeated games using cryptographic assumptions, extending to graphical games and defining a computational subgame-perfect equilibrium.
Findings
Polynomial-time algorithm for approximate Nash equilibria
Applicability to graphical games with constant degree
Efficient computation of computational subgame-perfect equilibrium
Abstract
We study the problem of computing an -Nash equilibrium in repeated games. Earlier work by Borgs et al. [2010] suggests that this problem is intractable. We show that if we make a slight change to their model---modeling the players as polynomial-time Turing machines that maintain state ---and make some standard cryptographic hardness assumptions (the existence of public-key encryption), the problem can actually be solved in polynomial time. Our algorithm works not only for games with a finite number of players, but also for constant-degree graphical games. As Nash equilibrium is a weak solution concept for extensive form games, we additionally define and study an appropriate notion of a subgame-perfect equilibrium for computationally bounded players, and show how to efficiently find such an equilibrium in repeated games (again, making standard cryptographic hardness…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGame Theory and Applications · Computability, Logic, AI Algorithms · Logic, Reasoning, and Knowledge
