Hysteresis effects of changing parameters of noncooperative games

TL;DR

This paper applies a statistical physics approach to noncooperative game theory, revealing hysteresis effects where gradual parameter changes lead to different equilibrium paths, including improved outcomes through incremental taxation.

Contribution

It introduces a novel adaptation of Jaynes' method to analyze equilibrium dependence on game parameters, highlighting hysteresis phenomena in bounded rational games.

Findings

Gradual tax imposition shifts players from poor to better equilibria.

Removing taxes does not necessarily revert to original equilibrium, showing hysteresis.

The approach uncovers path-dependent equilibrium transitions in game settings.

Abstract

We adapt the method used by Jaynes to derive the equilibria of statistical physics to instead derive equilibria of bounded rational game theory. We analyze the dependence of these equilibria on the parameters of the underlying game, focusing on hysteresis effects. In particular, we show that by gradually imposing individual-specific tax rates on the players of the game, and then gradually removing those taxes, the players move from a poor equilibrium to one that is better for all of them.