• Open Access

Correlation of Positive and Negative Reciprocity Fails to Confer an Evolutionary Advantage: Phase Transitions to Elementary Strategies

Attila Szolnoki and Matjaž Perc
Phys. Rev. X 3, 041021 – Published 27 November 2013

Abstract

Economic experiments reveal that humans value cooperation and fairness. Punishing unfair behavior is therefore common, and according to the theory of strong reciprocity, it is also directly related to rewarding cooperative behavior. However, empirical data fail to confirm that positive and negative reciprocity are correlated. Inspired by this disagreement, we determine whether the combined application of reward and punishment is evolutionarily advantageous. We study a spatial public goods game, where in addition to the three elementary strategies of defection, rewarding, and punishment, a fourth strategy that combines the latter two competes for space. We find rich dynamical behavior that gives rise to intricate phase diagrams where continuous and discontinuous phase transitions occur in succession. Indirect territorial competition, spontaneous emergence of cyclic dominance, as well as divergent fluctuations of oscillations that terminate in an absorbing phase are observed. Yet, despite the high complexity of solutions, the combined strategy can survive only in very narrow and unrealistic parameter regions. Elementary strategies, either in pure or mixed phases, are much more common and likely to prevail. Our results highlight the importance of patterns and structure in human cooperation, which should be considered in future experiments.

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  • Received 18 August 2013

DOI:https://doi.org/10.1103/PhysRevX.3.041021

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Authors & Affiliations

Attila Szolnoki1 and Matjaž Perc2

  • 1Institute of Technical Physics and Materials Science, Research Centre for Natural Sciences, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary
  • 2Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia

Popular Summary

One of the fundamental traits that set us apart from other animal species is our remarkable ability for cooperation with biologically unrelated other individuals. To explain the emergence and prevalence of this human trait has been one of the big challenges for social science. One of the theories is the so-called strong reciprocity hypothesis: If someone is kind to us, we tend to be kind in return. Similarly, if someone is unfair or exploitative, we tend to retaliate without much sympathy or stop cooperating. And, these two tendencies, or positive and negative reciprocity, are thought to be correlated to give us optimal evolutionary predispositions for cooperation. Recent human experiments, however, appear to reject this hypothesis, and our everyday experiences leave us with the impression that most people tend to either reward success or punish unfairness, but seldom do both. Which should we then believe or doubt, the hypothesis, or the conclusion of the human experiments? In this paper, we lend significant support to the latter with statistical physical simulations of evolutionary game models involving different reciprocity scenarios.

Our models are based on the so-called public goods games that involve both cooperators and defectors. Cooperators consist of three distinct groups, those that practice only the positive or negative reciprocity strategy and those that practice both, and all contribute to “the public goods,” while defectors contribute nothing. Defectors and cooperators are homogeneously distributed among the total population, and the former receive reward from an even distribution of the overall public goods, but also punishment (or a “fine”) from their cooperator neighbors that practice negative reciprocity. Both cooperators and defectors may change their strategy based on the payoffs they receive.

The question we focus on is whether practicing both positive and negative reciprocity strategies simultaneously confers an evolutionary advantage to individuals adopting such a correlated strategy. Through Monte Carlo simulations of the game playing, our model at once predicts both the emergence of a range of social behaviors, including indirect territorial competition and spontaneous emergence of cyclic dominance, and the very limited presence of the correlated strategy in very narrow and rather unrealistic parameter regions. Either only rewarding or only punishing is far superior and more effective in deterring defection.

We hope that our work will inspire more interdisciplinary theoretical and experimental work aimed at advancing our understanding of the evolution of human cooperation. The richness of our model in terms of exhibiting fundamentally different “social behaviors” (or nonequilibrium phenomena) should also make it an interesting playground for those physicists whose focus is on fundamental nonequilibrium physics.

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Vol. 3, Iss. 4 — October - December 2013

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It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 3.0 License. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

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