Ex ante versus ex post equilibria in classical Bayesian games with a nonlocal resource

TL;DR

This paper explores the differences between ex ante and ex post equilibria in Bayesian games with nonlocal resources, revealing new game constructions and a novel game where these equilibria differ, highlighting quantum advantages.

Contribution

It provides a constructive method to identify Bayesian games with nonlocal advantages and introduces a new game where ex ante and ex post equilibria diverge.

Findings

Most constructed games have identical ex ante and ex post equilibria.

A new game based on Bell's theorem shows differing ex ante and ex post equilibria.

Abstract

We analyze the difference between ex ante and ex post equilibria in classical games played with the assistance of a nonlocal (quantum or no-signaling) resource. In physics, the playing of these games is known as performing bipartite Bell-type experiments. By analyzing the Clauser-Horn-Shimony-Holt game, we find a constructive procedure to find two-person Bayesian games with a nonlocal (i.e. no-signaling, and, in many cases, quantum) advantage. Most games of this kind known from the literature can be constructed along this principle, and share the property that their relevant ex ante equilibria are ex post equilibria as well. We introduce a new type of game, based on the Bell-theorem by V\'ertesi and Bene, which does not have the latter property: the ex ante and ex post equilibria differ.