Behavioral Diversity in Voluntarily Separable Repeated Prisoner's Dilemma

29 Pages Posted: 14 Feb 2012 Last revised: 19 Feb 2012

See all articles by Takako Fujiwara-Greve

Takako Fujiwara-Greve

Keio University - Faculty of Economics

Masahiro Okuno-Fujiwara

University of Tokyo - Faculty of Economics

Date Written: January 31, 2012

Abstract

In the literature of voluntarily repeated Prisoner's Dilemma type games with no information flow, the focus is on how long-term cooperation is established. In this paper we investigate how non-cooperative and cooperative players co-exist. In many incomplete information versions of a similar model, inherently non-cooperative players are assumed to exist in the society, but their long-run fitness has not been analyzed. In reality and in experiments, we also observe that some people are cooperative, while others never cooperate. We show that, although defect-and-run type strategies are vulnerable to invasion of trust-building strategies (which defect initially but cooperate later among themselves), distributions of both types of strategies can be evolutionarily stable under equilibrium entrants. Moreover, the bimorphic equilibrium of the most cooperative strategy and the most myopic strategy exists under any payoff parameter combination, while bimorphic equilibria consisting only of cooperative (trust-building) strategies may not exist. In terms of payoffs, the bimorphic equilibrium of contrary strategies is equivalent to the equilibrium of infinitely many trust-building strategies. Both equilibria confirm the persistent presence of defectors.

Keywords: behavioral diversity, evolutionary stability, equilibrium entrants, voluntary separation, repeated Prisoner's Dilemma

JEL Classification: C73

Suggested Citation

Fujiwara-Greve, Takako and Okuno-Fujiwara, Masahiro, Behavioral Diversity in Voluntarily Separable Repeated Prisoner's Dilemma (January 31, 2012). Available at SSRN: https://ssrn.com/abstract=2005115 or http://dx.doi.org/10.2139/ssrn.2005115

Takako Fujiwara-Greve (Contact Author)

Keio University - Faculty of Economics ( email )

2-15-45 Mita, Ninato-ku
Tokyo 1088345
Japan

Masahiro Okuno-Fujiwara

University of Tokyo - Faculty of Economics ( email )

7-3-1 Hongo, Bunkyo-ku
Tokyo 113-0033
Japan

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