Sampling Logit Equilibrium and Endogenous Payoff Distortion

TL;DR

This paper introduces the sampling logit equilibrium (SLE), a new concept for population games where agents make decisions based on finite samples, blending sampling noise with stochastic choice to analyze equilibrium shifts.

Contribution

It proposes the SLE framework, linking finite sampling effects to equilibrium behavior and providing a new way to understand payoff distortions in population games.

Findings

Finite sampling can systematically shift equilibrium outcomes.

Large sample approximations relate SLE to distorted logit equilibria.

Sampling noise influences equilibrium selection effects.

Abstract

We introduce the sampling logit equilibrium (SLE), a stationary concept for population games in which agents evaluate actions using a finite sample of opponents' plays and respond according to a logit choice rule. This framework combines informational frictions from finite sampling with stochastic choice. When the sample size is large, SLE is well approximated by a logit equilibrium of a virtual game whose payoffs incorporate explicit distortion terms generated by sampling noise. Examples illustrate how finite sampling can systematically shift equilibrium behavior and generate equilibrium selection effects.