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Equilibria analysis in social dilemma games with Skinnerian agents

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Abstract

Different disciplines have analyzed binary choices to model collective behavior in human systems. Several situations in which social dilemma arise can be modeled as N-person prisoner’s dilemma games including homeland security, public goods, international political economy among others. The purpose of this study is to develop an analytical solution to the N-person prisoner’s dilemma game when boundedly rational agents interact in a population. Previous studies in the literature consider the case in which cooperators and defectors have the same learning factors. We obtain an analytical equation to find equilibria in the N-person prisoner’s dilemma game in the general case when agents have different learning factors. We also introduce a more realistic approach where probability values are bounded between zero and one and therefore eliminates the possibility of infeasible probability values. Since no analytic solution can be derived in this case, agent based simulation is used to analyze the asymptotic behavior of the resulted dynamical system.

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Authors and Affiliations

  1. Psychology Department, University of Torino, 10124, Turin, Italy

    Ugo Merlone

  2. Systems and Industrial Engineering Department, University of Arizona, Tucson, AZ, 85721-0020, USA

    Daren R. Sandbank

  3. Department of Applied Mathematics, University of Pécs, Ifjúság u. 6, 7624, Pécs, Hungary

    Ferenc Szidarovszky

Authors
  1. Ugo Merlone
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  2. Daren R. Sandbank
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  3. Ferenc Szidarovszky
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Correspondence to Ugo Merlone.

Additional information

This work has been performed within the activity of the PRIN project "Local interactions and global dynamics in economics and finance: models and tools”, MIUR, Italy, and under the auspices of COST Action IS1104 “The EU in the new complex geography of economic systems: models, tools and policy evaluation.”

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Merlone, U., Sandbank, D.R. & Szidarovszky, F. Equilibria analysis in social dilemma games with Skinnerian agents. Mind Soc 12, 219–233 (2013). https://doi.org/10.1007/s11299-013-0116-6

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  • DOI: https://doi.org/10.1007/s11299-013-0116-6

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