Selection problems in Large Deviations in Games under the logit choice protocol

TL;DR

This paper investigates large deviations in coordination games with the logit choice protocol, addressing whether different limiting processes yield the same properties, and provides definitive answers to these selection problems.

Contribution

It reformulates an open question about large deviations in game theory as PDE selection problems and offers conclusive solutions.

Findings

Clarifies the relationship between small noise and large population limits in large deviations.

Provides definitive answers to PDE selection problems in the context of coordination games.

Advances understanding of large deviations under the logit choice protocol.

Abstract

We study large deviations in coordination games under the logit choice protocol. A major open question that [10,11] posed is whether large deviations properties under the small noise double limit and the large population double limit are identical or not. We rephrase this open question in the PDE language as some selection problems, and we provide some definitive answers to these problems.