Cooperation in repeated interactions: A systematic review of Centipede game experiments, 1992–2016

ABSTRACT

Cooperation is a fundamental form of social interaction, and turn-taking reciprocity one of its most familiar manifestations. The Centipede game provides a formal model of such alternating reciprocal cooperation, but a backward induction (BI) argument appears to prove logically that instrumentally rational players would never cooperate in this way. A systematic review of experimental research reveals that human decision makers cooperate frequently in this game, except under certain extreme conditions. Several game, situational, and individual difference variables have been investigated for their influence on cooperation. The most influential are aspects of the payoff function (especially the social gain from cooperation and the risk associated with a cooperative move), the number of players, repetitions of the game, group vs. individual decisions, and players’ social value orientations (SVOs). Our review of experimental evidence suggests that other-regarding preferences, including prosocial behavioural dispositions and collective rationality, provide the most powerful explanation for cooperation.

KEYWORDS:

• Backward induction
• Centipede game
• cooperation
• game theory
• reciprocity

Acknowledgements

We are grateful to the Leicester Judgment and Decision Making Endowment Fund (Grant RM43G0176) and to the Friedrich Naumann Foundation for Freedom (postgraduate research grant) for support in the preparation of this article. We also wish to thank James Cox, Astrid Gamba, Anke Gerber, Werner Güth, Toshiji Kawagoe, Chloé Le Coq, Steven Levitt, Zacharias Maniadis, Christopher McIntosh, Ryan Murphy, Gavin Nachbar, Rosemarie Nagel, Ignacio Palacios-Huerta, Jim Parco, Amnon Rapoport, Tobias Regner, James Tremewan, and Ruey-Yun Horng for their provision of information, materials, and data sets from previous studies.

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Notes

¹ Inclusion criteria for Figures 3 and 4: (a) Published in peer-reviewed journal or book; (b) experiment conducted using the direct response method (as opposed to strategy method) for response elicitation; and (c) all quantitative measures displayed in figures were available to the authors.

Additional information

Funding

This work was supported by the Leicester Judgment and Decision Making Endowment Fund: [Grant Number RM43G0176]; Friedrich Naumann Foundation for Freedom.