Complementarities between Mathematical and Computational Modeling: The Case of the Repeated Prisoners' Dilemma

Xavier Vilà

UFAE and IAE Working Papers from Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC)

Abstract: We study the properties of the well known Replicator Dynamics when applied to a finitely repeated version of the Prisoners' Dilemma game. We characterize the behavior of such dynamics under strongly simplifying assumptions (i.e. only 3 strategies are available) and show that the basin of attraction of defection shrinks as the number of repetitions increases. After discussing the difficulties involved in trying to relax the 'strongly simplifying assumptions' above, we approach the same model by means of simulations based on genetic algorithms. The resulting simulations describe a behavior of the system very close to the one predicted by the replicator dynamics without imposing any of the assumptions of the mathematical model. Our main conclusion is that mathematical and computational models are good complements for research in social sciences. Indeed, while computational models are extremely useful to extend the scope of the analysis to complex scenarios hard to analyze mathematically, formal models can be useful to verify and to explain the outcomes of computational models.

Keywords: Computational Economics; Model-To-Model Analysis; Genetic Algorithms; Evolutionary Game Theory; Prisoners' Dilemma (search for similar items in EconPapers)
JEL-codes: C63 C73 (search for similar items in EconPapers)
Pages: 12
Date: 2010-10-27
New Economics Papers: this item is included in nep-cmp, nep-evo and nep-hpe
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Persistent link: https://EconPapers.repec.org/RePEc:aub:autbar:848.10

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