Quantal Response Equilibria in Binary Choice Games on Graphs

TL;DR

This paper develops equations for static and dynamic quantal response equilibria in noisy binary choice games on various graph topologies, linking them to phase transition phenomena and evolutionary game dynamics.

Contribution

It introduces explicit equations for QRE on arbitrary graphs and noise distributions, extending prior models and connecting to phase transition analysis in statistical physics.

Findings

Explicit QRE equations for non-directed graphs in the annealed approximation

Equivalence of special cases to earlier literature models

Demonstration of phase transition effects similar to Ising models

Abstract

Static and dynamic equilibria in noisy binary choice games on graphs are considered. Equations defining static quantal response equilibria (QRE) for binary choice games on graphs with arbitrary topology and noise distribution are written. It is shown that in the special cases of complete graph and arbitrary noise distribution, and circular and star topology and logistic noise distribution the resulting equations can be cast in the form coinciding with that derived in the earlier literature. Explicit equations QRE for non-directed graphs in the annealed approximation are derived. It is shown that the resulting effect on the phase transition is the same as found in the literature on phase transition in the Ising model on graphs in the same approximation.Evolutionary noisy binary choice game having the earlier described QRE as its stationary equilibria in the mean field approximation is constructed using the formalism of master equation.