Evolutionary Dynamics of the Spatial Prisoner’s Dilemma with Single and Multi-Behaviors: A Multi-Agent Application

Silva, Carla; Pereira, Welma; Knotek, Jan; Campos, Pedro

doi:10.1007/978-3-642-14788-3_49

Cited by 1 publication

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“…This is a Pavlovian type of agent, introduced by D. and V. Kraines in [8], which has a limited forecast of the game, and react myopically. Despite that this kind of behavior has been used in many works, specially through simulations, see [1,17,18], a theoretical analysis is lack, and we provide here the corresponding dynamics whenever finitely many agents are involved. This strategic update has an independent interest, and we study here their main properties.…”

Section: Introductionmentioning

confidence: 99%

A Game Theoretic Model of Wealth Distribution

2018

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In this work we consider an agent based model in order to study the wealth distribution problem where the interchange is determined with a symmetric zero sum game. Simultaneously, the agents update their way of play trying to learn the optimal one. Here, the agents use mixed strategies. We study this model using both simulations and theoretical tools. We derive the equations for the learning mechanism, and we show that the 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. If the equilibrium is a pure strategy, the wealth distribution is fixed after some transient time, and those players which are close to optimal strategy are richer. When the game has an equilibrium in mixed strategies, the stationary wealth distribution is close to a Gamma distribution with variance depending on the coefficients of the game matrix. We compute theoretically their second moment in this case.

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