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Games 2015, 6(4), 438-457; doi:10.3390/g6040438

Indirect Reciprocity with Optional Interactions and Private Information

1,†
,
1,2,3,†
and
1,2,4,*
1
Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, MA 02138, USA
2
Department of Mathematics, Harvard University, One Oxford Street, Cambridge, MA 02138, USA
3
National Institute for Mathematical Sciences, Daejeon 34047, Korea
4
Department of Organismic and Evolutionary Biology, Harvard University, 26 Oxford Street, Cambridge, MA 02138, USA
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Academic Editor: Ulrich Berger
Received: 19 June 2015 / Revised: 17 September 2015 / Accepted: 24 September 2015 / Published: 30 September 2015
(This article belongs to the Special Issue Cooperation, Trust, and Reciprocity)
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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. View Full-Text
Keywords: indirect reciprocity; cooperation; evolutionary dynamics indirect reciprocity; cooperation; evolutionary dynamics
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Olejarz, J.; Ghang, W.; Nowak, M.A. Indirect Reciprocity with Optional Interactions and Private Information. Games 2015, 6, 438-457.

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