Using Simulated Annealing to Calculate the Trembles of Trembling Hand Perfection

TL;DR

This paper explores how Markov chain Monte Carlo methods, particularly simulated annealing, can be used to compute Nash equilibria and relates trembles in these algorithms to trembling hand perfection in game theory.

Contribution

It demonstrates the connection between simulated annealing algorithms and trembling hand perfection, offering a novel perspective on equilibrium computation.

Findings

MCMC algorithms can compute Nash equilibria effectively.

Trembles in simulated annealing relate to trembling hand perfection.

The approach bridges optimization algorithms and game-theoretic refinements.

Abstract

Within the literature on non-cooperative game theory, there have been a number of attempts to propose logorithms which will compute Nash equilibria. Rather than derive a new algorithm, this paper shows that the family of algorithms known as Markov chain Monte Carlo (MCMC) can be used to calculate Nash equilibria. MCMC is a type of Monte Carlo simulation that relies on Markov chains to ensure its regularity conditions. MCMC has been widely used throughout the statistics and optimization literature, where variants of this algorithm are known as simulated annealing. This paper shows that there is interesting connection between the trembles that underlie the functioning of this algorithm and the type of Nash refinement known as trembling hand perfection.