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Indirect Reciprocity with Optional Interactions and Private Information

by 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
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: Ulrich Berger
Games 2015, 6(4), 438-457; https://doi.org/10.3390/g6040438
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)
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
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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. https://doi.org/10.3390/g6040438

AMA Style

Olejarz J, Ghang W, Nowak MA. Indirect Reciprocity with Optional Interactions and Private Information. Games. 2015; 6(4):438-457. https://doi.org/10.3390/g6040438

Chicago/Turabian Style

Olejarz, Jason; Ghang, Whan; Nowak, Martin A. 2015. "Indirect Reciprocity with Optional Interactions and Private Information" Games 6, no. 4: 438-457. https://doi.org/10.3390/g6040438

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