Mind & Society

, Volume 12, Issue 2, pp 219–233 | Cite as

Equilibria analysis in social dilemma games with Skinnerian agents

  • Ugo MerloneEmail author
  • Daren R. Sandbank
  • Ferenc Szidarovszky


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.


Social dilemmas Binary games Bounded rationality Agent based simulation 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Ugo Merlone
    • 1
    Email author
  • Daren R. Sandbank
    • 2
  • Ferenc Szidarovszky
    • 3
  1. 1.Psychology DepartmentUniversity of TorinoTurinItaly
  2. 2.Systems and Industrial Engineering DepartmentUniversity of ArizonaTucsonUSA
  3. 3.Department of Applied MathematicsUniversity of PécsPécsHungary

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