A Game Theoretic Model of Wealth Distribution

RODRIGUEZ CARTABIA, MAURO; RODRIGUEZ CARTABIA, MAURO; SAINTIER, NICOLAS; SAINTIER, NICOLAS; PINASCO, JUAN PABLO; PINASCO, JUAN PABLO

Dynamic Games and Applications

springer

Año: 2018 vol. 3

2153-0785

In this work we consider an agent based model in order to study the wealth distributionproblem where the interchange is determined with a symmetric zero sum game. Simultaneously, theagents update their way of play trying to learn the optimal one. Here, the agents use mixedstrategies. We study this model using both simulations and theoretical tools. We derive the equations for the learning mechanism, and we show thatthe mean strategy of the population satisfies an equation close to the classical replicator equation.Concerning the wealth distribution, there are two interesting situations depending on the equilibrium of the game. For pure strategies equilibria, the wealth distribution is fixed after some transient time, and those players which initially were close to the optimal strategy are richer. When the gamehas an equilibrium in mixed strategies, the stationary wealth distribution is close to a Gamma distribution withvariance depending on the coefficients of the game matrix. We compute theoretically theirsecond moment in this case.