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Competitive Centipede Games: Zero-End Payoffs and Payoff Inequality Deter Reciprocal Cooperation

Author

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  • Eva M. Krockow

    (Department of Neuroscience, Psychology and Behaviour, University of Leicester, Leicester LE1 7RH, UK)

  • Briony D. Pulford

    (Department of Neuroscience, Psychology and Behaviour, University of Leicester, Leicester LE1 7RH, UK)

  • Andrew M. Colman

    (Department of Neuroscience, Psychology and Behaviour, University of Leicester, Leicester LE1 7RH, UK)

Abstract

Reciprocal cooperation can be studied in the Centipede game, in which two players alternate in choosing between a cooperative GO move and a non-cooperative STOP move. GO sustains the interaction and increases the player pair’s total payoff while incurring a small personal cost; STOP terminates the interaction with a favorable payoff to the defector. We investigated cooperation in four Centipede games differing in their payoffs at the game’s end (positive versus zero) and payoff difference between players (moderate versus high difference). The games shared the same game-theoretic solution, therefore they should have elicited identical decision patterns, according to orthodox game theory. Nevertheless, both zero-end payoffs and high payoff inequality were found to reduce cooperation significantly. Contrary to previous predictions, combining these two factors in one game resulted in a slight weakening of their independent deterrent effects. These findings show that small changes in the payoff function have large and significant effects on cooperation, and that the effects do not combine synergistically.

Suggested Citation

  • Eva M. Krockow & Briony D. Pulford & Andrew M. Colman, 2015. "Competitive Centipede Games: Zero-End Payoffs and Payoff Inequality Deter Reciprocal Cooperation," Games, MDPI, vol. 6(3), pages 1-11, August.
    • Handle: RePEc:gam:jgames:v:6:y:2015:i:3:p:262-272:d:54381
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    References listed on IDEAS

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    1. Ryan O. Murphy & Amnon Rapoport & James E. Parco, 2004. "Population Learning of Cooperative Behavior in a Three-Person Centipede Game," Rationality and Society, , vol. 16(1), pages 91-120, February.
    2. McKelvey, Richard D & Palfrey, Thomas R, 1992. "An Experimental Study of the Centipede Game," Econometrica, Econometric Society, vol. 60(4), pages 803-836, July.
    3. Ryan Murphy & Amnon Rapoport & James Parco, 2006. "The breakdown of cooperation in iterative real-time trust dilemmas," Experimental Economics, Springer;Economic Science Association, vol. 9(2), pages 147-166, June.
    4. ., 1998. "Experimiental Economics," Chapters, in: John B. Davis & D. W. Hands & Uskali Mäki (ed.), The Handbook of Economic Methodology, chapter 36, Edward Elgar Publishing.
    5. Elchanan Ben-Porath, 1997. "Rationality, Nash Equilibrium and Backwards Induction in Perfect-Information Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(1), pages 23-46.
    6. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
    7. Bolle, Friedel, 1990. "High reward experiments without high expenditure for the experimenter?," Journal of Economic Psychology, Elsevier, vol. 11(2), pages 157-167, June.
    8. Fey, Mark & McKelvey, Richard D & Palfrey, Thomas R, 1996. "An Experimental Study of Constant-Sum Centipede Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(3), pages 269-287.
    9. Zauner, Klaus G., 1999. "A Payoff Uncertainty Explanation of Results in Experimental Centipede Games," Games and Economic Behavior, Elsevier, vol. 26(1), pages 157-185, January.
    10. Binmore, Ken, 1987. "Modeling Rational Players: Part I," Economics and Philosophy, Cambridge University Press, vol. 3(2), pages 179-214, October.
    11. Aumann, Robert J., 1998. "On the Centipede Game," Games and Economic Behavior, Elsevier, vol. 23(1), pages 97-105, April.
    12. Philip J. Reny, 1992. "Rationality in Extensive-Form Games," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 103-118, Fall.
    13. Rapoport, Amnon & Stein, William E. & Parco, James E. & Nicholas, Thomas E., 2003. "Equilibrium play and adaptive learning in a three-person centipede game," Games and Economic Behavior, Elsevier, vol. 43(2), pages 239-265, May.
    14. James C. Cox & Duncan James, 2015. "On Replication and Perturbation of the McKelvey and Palfrey Centipede Game Experiment," Research in Experimental Economics, in: Replication in Experimental Economics, volume 18, pages 53-94, Emerald Group Publishing Limited.
    15. Robin Cubitt & Chris Starmer & Robert Sugden, 1998. "On the Validity of the Random Lottery Incentive System," Experimental Economics, Springer;Economic Science Association, vol. 1(2), pages 115-131, September.
    16. Droste, Edward & Kosfeld, Michael & Voorneveld, Mark, 2003. "Best-reply matching in games," Mathematical Social Sciences, Elsevier, vol. 46(3), pages 291-309, December.
    17. McDaniel, Tanga & Starmer, Chris, 1998. "Experimental economics and deception: A comment," Journal of Economic Psychology, Elsevier, vol. 19(3), pages 403-409, June.
    18. Rosenthal, Robert W., 1981. "Games of perfect information, predatory pricing and the chain-store paradox," Journal of Economic Theory, Elsevier, vol. 25(1), pages 92-100, August.
    19. James C. Cox & Duncan James, 2012. "Clocks and Trees: Isomorphic Dutch Auctions and Centipede Games," Econometrica, Econometric Society, vol. 80(2), pages 883-903, March.
    20. Kawagoe, Toshiji & Takizawa, Hirokazu, 2012. "Level-k analysis of experimental centipede games," Journal of Economic Behavior & Organization, Elsevier, vol. 82(2), pages 548-566.
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    Cited by:

    1. Eva M. Krockow & Masanori Takezawa & Briony D. Pulford & Andrew M. Colman & Samuel Smithers & Toshimasa Kita & Yo Nakawake, 2018. "Commitment-enhancing tools in Centipede games: Evidencing European–Japanese differences in trust and cooperation," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 13(1), pages 61-72, January.
    2. Briony D Pulford & Eva M Krockow & Andrew M Colman & Catherine L Lawrence, 2016. "Social Value Induction and Cooperation in the Centipede Game," PLOS ONE, Public Library of Science, vol. 11(3), pages 1-21, March.
    3. Krockow, Eva M. & Pulford, Briony D. & Colman, Andrew M., 2018. "Far but finite horizons promote cooperation in the Centipede game," Journal of Economic Psychology, Elsevier, vol. 67(C), pages 191-199.
    4. Wolfram Elsner, 2019. "Policy and state in complexity economics," Chapters, in: Nikolaos Karagiannis & John E. King (ed.), A Modern Guide to State Intervention, chapter 1, pages 13-48, Edward Elgar Publishing.
    5. repec:cup:judgdm:v:13:y:2018:i:1:p:61-72 is not listed on IDEAS

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