Indirect Reciprocity with Optional Interactions and Private Information

Jason Olejarz, Whan Ghang and Martin A. Nowak
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Jason Olejarz: Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, MA 02138, USA
Whan Ghang: Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, MA 02138, USA
Martin A. Nowak: Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, MA 02138, USA

Games, 2015, vol. 6, issue 4, 1-20

Abstract: We consider indirect reciprocity with optional interactions and private information. A game is offered between two players and accepted unless it is known that the other person is a defector. Whenever a defector manages to exploit a cooperator, his or her reputation is revealed to others in the population with some probability. Therefore, people have different private information about the reputation of others, which is a setting that is difficult to analyze in the theory of indirect reciprocity. Since a defector loses a fraction of his social ties each time he exploits a cooperator, he is less efficient at exploiting cooperators in subsequent rounds. We analytically calculate the critical benefit-to-cost ratio above which cooperation is successful in various settings. We demonstrate quantitative agreement with simulation results of a corresponding Wright–Fisher process with optional interactions and private information. We also deduce a simple necessary condition for the critical benefit-to-cost ratio.

Keywords: indirect reciprocity; cooperation; evolutionary dynamics (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

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