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Cooperation over finite horizons: A theory and experiments

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  • Ambrus, Attila
  • Pathak, Parag A.

Abstract

This paper shows that the presence of different types of players – those who only care about their own material payoffs and those who reciprocate others' contributions – can explain the robust features of observed contribution patterns in public good contribution games, even without the presence of asymmetric information. We show what conditions on reciprocity are sufficient for a unique perfect equilibrium, in which contributions are decreasing. Under these conditions, selfish players have enough future benefits to induce subsequent contributions by reciprocal players, and this incentive diminishes as the end of the game approaches. The model explains the puzzling restart effect and is consistent with various other empirical findings. We also report the results of a series of experiments, using a probabilistic continuation design in which after each set of 10-period games, the group is restarted with low probability. We find specific support for the theory in our data, including that selfish players (identified exogenously) stop contributing earlier than reciprocal players, as directly implied by the model.

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  • Ambrus, Attila & Pathak, Parag A., 2011. "Cooperation over finite horizons: A theory and experiments," Journal of Public Economics, Elsevier, vol. 95(7), pages 500-512.
    • Handle: RePEc:eee:pubeco:v:95:y:2011:i:7:p:500-512
    DOI: 10.1016/j.jpubeco.2010.11.016
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    1. Simon Gächter & Elke Renner, 2010. "The effects of (incentivized) belief elicitation in public goods experiments," Experimental Economics, Springer;Economic Science Association, vol. 13(3), pages 364-377, September.
    2. R. M Isaac & J. Walker & A. Williams, 2010. "Group Size and the Voluntary Provision of Public Goods: Experimental Evidence Utilizing Very Large Groups," Levine's Working Paper Archive 11, David K. Levine.
    3. McKelvey, Richard D & Palfrey, Thomas R, 1992. "An Experimental Study of the Centipede Game," Econometrica, Econometric Society, vol. 60(4), pages 803-836, July.
    4. Kreps, David M. & Milgrom, Paul & Roberts, John & Wilson, Robert, 1982. "Rational cooperation in the finitely repeated prisoners' dilemma," Journal of Economic Theory, Elsevier, vol. 27(2), pages 245-252, August.
    5. Ernst Fehr & Klaus M. Schmidt, 1999. "A Theory of Fairness, Competition, and Cooperation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 817-868.
    6. Blount, Sally, 1995. "When Social Outcomes Aren't Fair: The Effect of Causal Attributions on Preferences," Organizational Behavior and Human Decision Processes, Elsevier, vol. 63(2), pages 131-144, August.
    7. Andreoni, James, 1988. "Why free ride? : Strategies and learning in public goods experiments," Journal of Public Economics, Elsevier, vol. 37(3), pages 291-304, December.
    8. Guttman, Joel M, 1978. "Understanding Collective Action: Matching Behavior," American Economic Review, American Economic Association, vol. 68(2), pages 251-255, May.
    9. Stahl Dale O. & Wilson Paul W., 1995. "On Players' Models of Other Players: Theory and Experimental Evidence," Games and Economic Behavior, Elsevier, vol. 10(1), pages 218-254, July.
    10. Oriana Bandiera & Iwan Barankay & Imran Rasul, 2005. "Social Preferences and the Response to Incentives: Evidence from Personnel Data," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 120(3), pages 917-962.
    11. Claudia Keser & Frans Van Winden, 2000. "Conditional Cooperation and Voluntary Contributions to Public Goods," Scandinavian Journal of Economics, Wiley Blackwell, vol. 102(1), pages 23-39, March.
    12. David K. Levine, 1998. "Modeling Altruism and Spitefulness in Experiment," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 1(3), pages 593-622, July.
    13. Jehiel, Philippe, 2005. "Analogy-based expectation equilibrium," Journal of Economic Theory, Elsevier, vol. 123(2), pages 81-104, August.
    14. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
    15. Urs Fischbacher & Simon Gachter, 2010. "Social Preferences, Beliefs, and the Dynamics of Free Riding in Public Goods Experiments," American Economic Review, American Economic Association, vol. 100(1), pages 541-556, March.
    16. Martin Brown & Armin Falk & Ernst Fehr, 2004. "Relational Contracts and the Nature of Market Interactions," Econometrica, Econometric Society, vol. 72(3), pages 747-780, May.
    17. R. Mark Isaac & James M. Walker, 1988. "Group Size Effects in Public Goods Provision: The Voluntary Contributions Mechanism," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 103(1), pages 179-199.
    18. Drew Fudenberg & Eric Maskin, 1998. "The Folk Theorem for Repeated Games with Discounting and Incomplete Information," Levine's Working Paper Archive 224, David K. Levine.
    19. Ernst Fehr & Klaus M. Schmidt, "undated". "Theories of Fairness and Reciprocity - Evidence and Economic Applications," IEW - Working Papers 075, Institute for Empirical Research in Economics - University of Zurich.
    20. Isaac, R. Mark & Walker, James M. & Williams, Arlington W., 1994. "Group size and the voluntary provision of public goods : Experimental evidence utilizing large groups," Journal of Public Economics, Elsevier, vol. 54(1), pages 1-36, May.
    21. Croson, Rachel T. A., 1996. "Partners and strangers revisited," Economics Letters, Elsevier, vol. 53(1), pages 25-32, October.
    22. McCabe, Kevin A. & Rigdon, Mary L. & Smith, Vernon L., 2003. "Positive reciprocity and intentions in trust games," Journal of Economic Behavior & Organization, Elsevier, vol. 52(2), pages 267-275, October.
    23. Fischbacher, Urs & Gachter, Simon & Fehr, Ernst, 2001. "Are people conditionally cooperative? Evidence from a public goods experiment," Economics Letters, Elsevier, vol. 71(3), pages 397-404, June.
    24. R. Isaac & James Walker & Susan Thomas, 1984. "Divergent evidence on free riding: An experimental examination of possible explanations," Public Choice, Springer, vol. 43(2), pages 113-149, January.
    25. Abraham Neyman, 1999. "Cooperation in Repeated Games when the Number of Stages is Not Commonly Known," Econometrica, Econometric Society, vol. 67(1), pages 45-64, January.
    26. Dufwenberg, Martin & Kirchsteiger, Georg, 2004. "A theory of sequential reciprocity," Games and Economic Behavior, Elsevier, vol. 47(2), pages 268-298, May.
    27. Andreoni, James & Samuelson, Larry, 2006. "Building rational cooperation," Journal of Economic Theory, Elsevier, vol. 127(1), pages 117-154, March.
    28. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August.
    29. Takayama,Akira, 1985. "Mathematical Economics," Cambridge Books, Cambridge University Press, number 9780521314985, October.
    30. James C. Cox & Vjollca Sadiraj, 2007. "On Modeling Voluntary Contributions to Public Goods," Public Finance Review, , vol. 35(2), pages 311-332, March.
    31. Oliver Kim & Mark Walker, 1984. "The free rider problem: Experimental evidence," Public Choice, Springer, vol. 43(1), pages 3-24, January.
    32. Palfrey, Thomas R & Prisbrey, Jeffrey E, 1997. "Anomalous Behavior in Public Goods Experiments: How Much and Why?," American Economic Review, American Economic Association, vol. 87(5), pages 829-846, December.
    33. Sonnemans, Joep & Schram, Arthur & Offerman, Theo, 1999. "Strategic behavior in public good games: when partners drift apart," Economics Letters, Elsevier, vol. 62(1), pages 35-41, January.
    34. Drew Fudenberg & Eric Maskin, 2008. "The Folk Theorem In Repeated Games With Discounting Or With Incomplete Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 11, pages 209-230, World Scientific Publishing Co. Pte. Ltd..
    35. Cox, James C. & Friedman, Daniel & Gjerstad, Steven, 2007. "A tractable model of reciprocity and fairness," Games and Economic Behavior, Elsevier, vol. 59(1), pages 17-45, April.
    36. Charles R. Plott & Vernon L. Smith (ed.), 2008. "Handbook of Experimental Economics Results," Handbook of Experimental Economics Results, Elsevier, edition 1, volume 1, number 3.
    37. Charles R. Plott & Vernon L. Smith (ed.), 2008. "Handbook of Experimental Economics Results," Handbook of Experimental Economics Results, Elsevier, edition 1, volume 1, number 7.
    38. Andreoni, James & Petrie, Ragan, 2004. "Public goods experiments without confidentiality: a glimpse into fund-raising," Journal of Public Economics, Elsevier, vol. 88(7-8), pages 1605-1623, July.
    39. Radner, Roy, 1980. "Collusive behavior in noncooperative epsilon-equilibria of oligopolies with long but finite lives," Journal of Economic Theory, Elsevier, vol. 22(2), pages 136-154, April.
    40. Anderson, Simon P. & Goeree, Jacob K. & Holt, Charles A., 1998. "A theoretical analysis of altruism and decision error in public goods games," Journal of Public Economics, Elsevier, vol. 70(2), pages 297-323, November.
    41. Offerman, Theo & Sonnemans, Joep & Schram, Arthur, 1996. "Value Orientations, Expectations and Voluntary Contributions in Public Goods," Economic Journal, Royal Economic Society, vol. 106(437), pages 817-845, July.
    42. Andreoni, James, 1989. "Giving with Impure Altruism: Applications to Charity and Ricardian Equivalence," Journal of Political Economy, University of Chicago Press, vol. 97(6), pages 1447-1458, December.
    43. Joel Sobel, 1985. "A Theory of Credibility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(4), pages 557-573.
    44. Charles R. Plott & Vernon L. Smith (ed.), 2008. "Handbook of Experimental Economics Results," Handbook of Experimental Economics Results, Elsevier, edition 1, volume 1, number 4.
    45. Axel Ockenfels & Gary E. Bolton, 2000. "ERC: A Theory of Equity, Reciprocity, and Competition," American Economic Review, American Economic Association, vol. 90(1), pages 166-193, March.
    46. Rabin, Matthew, 1993. "Incorporating Fairness into Game Theory and Economics," American Economic Review, American Economic Association, vol. 83(5), pages 1281-1302, December.
    47. Charles R. Plott & Vernon L. Smith (ed.), 2008. "Handbook of Experimental Economics Results," Handbook of Experimental Economics Results, Elsevier, edition 1, volume 1, number 2.
    48. Charles R. Plott & Vernon L. Smith (ed.), 2008. "Handbook of Experimental Economics Results," Handbook of Experimental Economics Results, Elsevier, edition 1, volume 1, number 8.
    49. Charles R. Plott & Vernon L. Smith (ed.), 2008. "Handbook of Experimental Economics Results," Handbook of Experimental Economics Results, Elsevier, edition 1, volume 1, number 5.
    50. Tilman Klumpp, 2012. "Finitely Repeated Voluntary Provision of a Public Good," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 14(4), pages 547-572, August.
    51. Charles R. Plott & Vernon L. Smith (ed.), 2008. "Handbook of Experimental Economics Results," Handbook of Experimental Economics Results, Elsevier, edition 1, volume 1, number 1.
    52. Brandts, Jordi & Schram, Arthur, 2001. "Cooperation and noise in public goods experiments: applying the contribution function approach," Journal of Public Economics, Elsevier, vol. 79(2), pages 399-427, February.
    53. Charles R. Plott & Vernon L. Smith (ed.), 2008. "Handbook of Experimental Economics Results," Handbook of Experimental Economics Results, Elsevier, edition 1, volume 1, number 6.
    54. Urs Fischbacher, 2007. "z-Tree: Zurich toolbox for ready-made economic experiments," Experimental Economics, Springer;Economic Science Association, vol. 10(2), pages 171-178, June.
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    Keywords

    Public goods; Restart effect;

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