Eur. Phys. J. B 53, 267-272 (2006)
https://doi.org/10.1140/epjb/e2006-00355-x

Statistical equilibrium in simple exchange games I

Methods of solution and application to the Bennati-Dragulescu-Yakovenko (BDY) game

¹ Department of Advanced Sciences and Technology, Laboratory on Complex Systems, East Piedmont University, via Bellini 25 g, 15100 Alessandria, Italy
² IMEM-CNR, Physics Department, Genoa University, via Dodecaneso 33, 16146 Genoa, Italy
³ INFN, Physics Department, Genoa University, via Dodecaneso 33, 16146 Genoa, Italy

Corresponding author: ^a scalas@unipmn.it

Received: 31 May 2006
Revised: 3 August 2006
Published online: 27 September 2006

Abstract

Simple stochastic exchange games are based on random allocation of finite resources. These games are Markov chains that can be studied either analytically or by Monte Carlo simulations. In particular, the equilibrium distribution can be derived either by direct diagonalization of the transition matrix, or using the detailed balance equation, or by Monte Carlo estimates. In this paper, these methods are introduced and applied to the Bennati-Dragulescu-Yakovenko (BDY) game. The exact analysis shows that the statistical-mechanical analogies used in the previous literature have to be revised.