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Games 2018, 9(4), 100; https://doi.org/10.3390/g9040100

Evolution of Groupwise Cooperation: Generosity, Paradoxical Behavior, and Non-Linear Payoff Functions

1
Department of Biological Sciences, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan
2
Division of Natural Resource Economics, Graduate School of Agriculture, Kyoto University, Oiwake-cho, Kitashirakawa, Sakyo-ku, Kyoto 606-8502, Japan
3
Key Lab of Animal Ecology and Conservation Biology, Institute of Zoology, Chinese Academy of Science, Datun Road, Chaoyang, Beijing 100101, China
4
School of Economics and Management, Kochi University of Technology, Kochi 780-8515, Japan
5
Meiji Institute for Advanced Study of Mathematical Sciences, Meiji Univeristy, Nakano 4-21-1, Nakano-ku, Tokyo 164-8525, Japan
*
Author to whom correspondence should be addressed.
Received: 29 September 2018 / Revised: 8 November 2018 / Accepted: 13 November 2018 / Published: 10 December 2018
(This article belongs to the Special Issue The Evolution of Cooperation in Game Theory and Social Simulation)
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Abstract

Evolution of cooperation by reciprocity has been studied using two-player and n-player repeated prisoner’s dilemma games. An interesting feature specific to the n-player case is that players can vary in generosity, or how many defections they tolerate in a given round of a repeated game. Reciprocators are quicker to detect defectors to withdraw further cooperation when less generous, and better at maintaining a long-term cooperation in the presence of rare defectors when more generous. A previous analysis on a stochastic evolutionary model of the n-player repeated prisoner’s dilemma has shown that the fixation probability of a single reciprocator in a population of defectors can be maximized for a moderate level of generosity. However, the analysis is limited in that it considers only tit-for-tat-type reciprocators within the conventional linear payoff assumption. Here we extend the previous study by removing these limitations and show that, if the games are repeated sufficiently many times, considering non-tit-for-tat type strategies does not alter the previous results, while the introduction of non-linear payoffs sometimes does. In particular, under certain conditions, the fixation probability is maximized for a “paradoxical” strategy, which cooperates in the presence of fewer cooperating opponents than in other situations in which it defects. View Full-Text
Keywords: evolutionary game theory; cooperation; generosity; repeated game; prisoner’s dilemma evolutionary game theory; cooperation; generosity; repeated game; prisoner’s dilemma
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Kurokawa, S.; Wakano, J.Y.; Ihara, Y. Evolution of Groupwise Cooperation: Generosity, Paradoxical Behavior, and Non-Linear Payoff Functions. Games 2018, 9, 100.

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