A quantum protocol for sampling correlated equilibria unconditionally and without a mediator

TL;DR

This paper introduces a quantum communication protocol that enables players to achieve correlated equilibria in 2-player games without needing a trusted mediator, unconditionally leveraging quantum information processing.

Contribution

It demonstrates that quantum communication can replace mediators in game theory, achieving correlated equilibria unconditionally and without computational assumptions.

Findings

Quantum communication enables unconditionally achieving correlated equilibria.

The protocol uses quantum weak coin flipping for secure coordination.

Players' payoffs match or exceed those in classical correlated equilibria.

Abstract

A correlated equilibrium is a fundamental solution concept in game theory that enjoys many desirable properties. However, it requires a trusted mediator, which is a major drawback in many practical applications. A computational solution to this problem was proposed by Dodis, Halevi and Rabin. They extended the original game by adding an initial communication stage and showed that any correlated strategy for 2-player games can be achieved, provided that the players are computationally bounded. In this paper, we show that if the players can communicate via a quantum channel before the game, then any correlated equilibrium for 2-player games can be achieved, without a trusted mediator and unconditionally. This provides another example of a major advantage of quantum information processing. More precisely, we prove that for any correlated equilibrium p of a strategic game G, there exists an extended game (with a quantum communication initial stage) Q with an efficiently computable approximate Nash equilibrium q, such that the expected payoff for both players in q is at least as high as in p. The main cryptographic tool used in the construction is the quantum weak coin flipping protocol of Mochon.