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      Power Asymmetries and Punishment in a Prisoner’s Dilemma with Variable Cooperative Investment

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          Abstract

          In many two-player games, players that invest in punishment finish with lower payoffs than those who abstain from punishing. These results question the effectiveness of punishment at promoting cooperation, especially when retaliation is possible. It has been suggested that these findings may stem from the unrealistic assumption that all players are equal in terms of power. However, a previous empirical study which incorporated power asymmetries into an iterated prisoner's dilemma (IPD) game failed to show that power asymmetries stabilize cooperation when punishment is possible. Instead, players cooperated in response to their partner cooperating, and punishment did not yield any additional increase in tendency to cooperate. Nevertheless, this previous study only allowed an all-or-nothing–rather than a variable–cooperation investment. It is possible that power asymmetries increase the effectiveness of punishment from strong players only when players are able to vary their investment in cooperation. We tested this hypothesis using a modified IPD game which allowed players to vary their investment in cooperation in response to being punished. As in the previous study, punishment from strong players did not increase cooperation under any circumstances. Thus, in two-player games with symmetric strategy sets, punishment does not appear to increase cooperation.

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          The neural basis of altruistic punishment.

          Dominique de Quervain, Urs Fischbacher, Valerie Treyer … (2004)
          Many people voluntarily incur costs to punish violations of social norms. Evolutionary models and empirical evidence indicate that such altruistic punishment has been a decisive force in the evolution of human cooperation. We used H2 15O positron emission tomography to examine the neural basis for altruistic punishment of defectors in an economic exchange. Subjects could punish defection either symbolically or effectively. Symbolic punishment did not reduce the defector's economic payoff, whereas effective punishment did reduce the payoff. We scanned the subjects' brains while they learned about the defector's abuse of trust and determined the punishment. Effective punishment, as compared with symbolic punishment, activated the dorsal striatum, which has been implicated in the processing of rewards that accrue as a result of goal-directed actions. Moreover, subjects with stronger activations in the dorsal striatum were willing to incur greater costs in order to punish. Our findings support the hypothesis that people derive satisfaction from punishing norm violations and that the activation in the dorsal striatum reflects the anticipated satisfaction from punishing defectors.
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            Via freedom to coercion: the emergence of costly punishment.

            Christoph Hauert, Arne Traulsen, Hannelore Brandt … (2007)
            In human societies, cooperative behavior in joint enterprises is often enforced through institutions that impose sanctions on defectors. Many experiments on so-called public goods games have shown that in the absence of such institutions, individuals are willing to punish defectors, even at a cost to themselves. Theoretical models confirm that social norms prescribing the punishment of uncooperative behavior are stable-once established, they prevent dissident minorities from spreading. But how can such costly punishing behavior gain a foothold in the population? A surprisingly simple model shows that if individuals have the option to stand aside and abstain from the joint endeavor, this paves the way for the emergence and establishment of cooperative behavior based on the punishment of defectors. Paradoxically, the freedom to withdraw from the common enterprise leads to enforcement of social norms. Joint enterprises that are compulsory rather than voluntary are less likely to lead to cooperation.
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              Positive interactions promote public cooperation.

              David Rand, Anna Dreber, Tore Ellingsen … (2009)
              The public goods game is the classic laboratory paradigm for studying collective action problems. Each participant chooses how much to contribute to a common pool that returns benefits to all participants equally. The ideal outcome occurs if everybody contributes the maximum amount, but the self-interested strategy is not to contribute anything. Most previous studies have found punishment to be more effective than reward for maintaining cooperation in public goods games. The typical design of these studies, however, represses future consequences for today's actions. In an experimental setting, we compare public goods games followed by punishment, reward, or both in the setting of truly repeated games, in which player identities persist from round to round. We show that reward is as effective as punishment for maintaining public cooperation and leads to higher total earnings. Moreover, when both options are available, reward leads to increased contributions and payoff, whereas punishment has no effect on contributions and leads to lower payoff. We conclude that reward outperforms punishment in repeated public goods games and that human cooperation in such repeated settings is best supported by positive interactions with others.
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                Author and article information

                Contributors
                Alex Mesoudi: Role: Editor
                Journal
                Journal ID (nlm-ta): PLoS One
                Journal ID (iso-abbrev): PLoS ONE
                Journal ID (publisher-id): plos
                Journal ID (pmc): plosone
                Title: PLoS ONE
                Publisher: Public Library of Science (San Francisco, CA USA )
                ISSN (Electronic): 1932-6203
                Publication date (Electronic): 18 May 2016
                Publication date Collection: 2016
                Volume: 11
                Issue: 5
                Electronic Location Identifier: e0155773
                Affiliations
                [1 ]CoMPLEX, Physics Building, Gower Place, University College London, London, WC1E 6BT, United Kingdom
                [2 ]Department of Economics, Drayton House, 30 Gordon Street, University College London, London, WC1H 0AX, United Kingdom
                [3 ]Institut de Biologie, Eco-Ethologie, Université de Neuchâtel, Neuchâtel, CH-2000, Switzerland
                [4 ]Department of Experimental Psychology, 26 Bedford Way, University College London, London, WC1H 0AP, United Kingdom
                University of Exeter, UNITED KINGDOM
                Author notes

                Competing Interests: The authors have declared that no competing interests exist.

                Conceived and designed the experiments: NR JB RB. Performed the experiments: JB BW. Analyzed the data: JB. Wrote the paper: NR JB RB.

                Article
                Publisher ID: PONE-D-16-08124
                DOI: 10.1371/journal.pone.0155773
                PMC ID: 4871419
                PubMed ID: 27191958
                SO-VID: e23380a7-41f9-4db3-bdc7-81e7ed4851e9
                Copyright © © 2016 Bone et al
                License:

                This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                History
                Date received : 25 February 2016
                Date accepted : 3 May 2016
                Page count
                Figures: 5, Tables: 6, Pages: 16
                Funding
                Funded by: funder-id http://dx.doi.org/10.13039/501100000288, Royal Society;
                Award Recipient :
                This study was funded by a Royal Society University Research Fellowship to NR.
                Categories
                Subject: Research Article
                Subject: Biology and Life Sciences
                Subject: Behavior
                Subject: Recreation
                Subject: Games
                Subject: Physical Sciences
                Subject: Mathematics
                Subject: Applied Mathematics
                Subject: Game Theory
                Subject: Physical Sciences
                Subject: Mathematics
                Subject: Applied Mathematics
                Subject: Game Theory
                Subject: Prisoner's Dilemma
                Subject: Biology and Life Sciences
                Subject: Behavior
                Subject: Social Sciences
                Subject: Economics
                Subject: Experimental Economics
                Subject: Biology and Life Sciences
                Subject: Parasitology
                Subject: Ectoparasites
                Subject: Biology and Life Sciences
                Subject: Neuroscience
                Subject: Cognitive Science
                Subject: Cognitive Psychology
                Subject: Language
                Subject: Biology and Life Sciences
                Subject: Psychology
                Subject: Cognitive Psychology
                Subject: Language
                Subject: Social Sciences
                Subject: Psychology
                Subject: Cognitive Psychology
                Subject: Language
                Subject: Physical Sciences
                Subject: Mathematics
                Subject: Statistics (Mathematics)
                Subject: Confidence Intervals
                Custom metadata
                Data Availability All relevant data are within the paper and its Supporting Information files.

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