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Learning in a multilateral bargaining experiment

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  • Fréchette, Guillaume R.

Abstract

This paper analyzes data from an investigation of a majoritarian bargaining experiment. A learning model is proposed to account for the evolution of play in this experiment. It is also suggested that an adjustment must be made to account for the panel structure of the data. Such adjustments have been used in other fields and are known to be important as unadjusted standard errors may be severely biased downward. These results indicate that this adjustment also has an important effect in this application. Furthermore, an efficient estimator that takes into account heterogeneity across players is proposed. A unique learning model to account for the paths of play under two different amendment rules cannot be rejected with the standard estimator with adjusted standard errors, however it can be rejected using the efficient estimator. The data and the estimated learning model suggest that after proposing "fair"Â divisions, subjects adapt and their proposals change rapidly in the treatment where uneven proposals are almost always accepted. Their beliefs in the estimated learning model are influenced by more than just the most recent outcomes.

Suggested Citation

  • Fréchette, Guillaume R., 2009. "Learning in a multilateral bargaining experiment," Journal of Econometrics, Elsevier, vol. 153(2), pages 183-195, December.
  • Handle: RePEc:eee:econom:v:153:y:2009:i:2:p:183-195
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    as
    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Gary Charness & Matthew Rabin, 2002. "Understanding Social Preferences with Simple Tests," The Quarterly Journal of Economics, Oxford University Press, vol. 117(3), pages 817-869.
    3. Ernst Fehr & Klaus M. Schmidt, 1999. "A Theory of Fairness, Competition, and Cooperation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 817-868.
    4. Erev, Ido & Roth, Alvin E, 1998. "Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria," American Economic Review, American Economic Association, vol. 88(4), pages 848-881, September.
    5. Baron, David P. & Ferejohn, John A., 1989. "Bargaining in Legislatures," American Political Science Review, Cambridge University Press, vol. 83(4), pages 1181-1206, December.
    6. Hausman, Jerry A & Wise, David A, 1978. "A Conditional Probit Model for Qualitative Choice: Discrete Decisions Recognizing Interdependence and Heterogeneous Preferences," Econometrica, Econometric Society, vol. 46(2), pages 403-426, March.
    7. Ham, John C. & Kagel, John H. & Lehrer, Steven F., 2005. "Randomization, endogeneity and laboratory experiments: the role of cash balances in private value auctions," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 175-205.
    8. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, June.
    9. Levitt, Steven D & Poterba, James M, 1999. "Congressional Distributive Politics and State Economic Performance," Public Choice, Springer, vol. 99(1-2), pages 185-216, April.
    10. Roth, Alvin E. & Erev, Ido, 1995. "Learning in extensive-form games: Experimental data and simple dynamic models in the intermediate term," Games and Economic Behavior, Elsevier, vol. 8(1), pages 164-212.
    11. Frã‰Chette, Guillaume R. & Kagel, John H. & Lehrer, Steven F., 2003. "Bargaining in Legislatures: An Experimental Investigation of Open versus Closed Amendment Rules," American Political Science Review, Cambridge University Press, vol. 97(2), pages 221-232, May.
    12. David J. Cooper & Susan Garvin & John H. Kagel, 1997. "Signalling and Adaptive Learning in an Entry Limit Pricing Game," RAND Journal of Economics, The RAND Corporation, vol. 28(4), pages 662-683, Winter.
    13. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
    14. 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.
    15. Olivier Armantier, 2006. "Do Wealth Differences Affect Fairness Considerations?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 391-429, May.
    16. John C. Ham, 1986. "Testing whether Unemployment Represents Intertemporal Labour Supply Behaviour," Review of Economic Studies, Oxford University Press, vol. 53(4), pages 559-578.
    17. Moulton, Brent R., 1986. "Random group effects and the precision of regression estimates," Journal of Econometrics, Elsevier, vol. 32(3), pages 385-397, August.
    18. Stahl, Dale O., 1996. "Boundedly Rational Rule Learning in a Guessing Game," Games and Economic Behavior, Elsevier, vol. 16(2), pages 303-330, October.
    19. Butler, J S & Moffitt, Robert, 1982. "A Computationally Efficient Quadrature Procedure for the One-Factor Multinomial Probit Model," Econometrica, Econometric Society, vol. 50(3), pages 761-764, May.
    20. Pepper, John V., 2002. "Robust inferences from random clustered samples: an application using data from the panel study of income dynamics," Economics Letters, Elsevier, vol. 75(3), pages 341-345, May.
    21. Binmore, K & Shaked, A & Sutton, J, 1985. "Testing Noncooperative Bargaining Theory: A Preliminary Study," American Economic Review, American Economic Association, vol. 75(5), pages 1178-1180, December.
    22. Cooper, David J. & Stockman, Carol Kraker, 2002. "Fairness and learning: an experimental examination," Games and Economic Behavior, Elsevier, vol. 41(1), pages 26-45, October.
    23. Armantier, Olivier, 2004. "Does observation influence learning?," Games and Economic Behavior, Elsevier, vol. 46(2), pages 221-239, February.
    24. Cheung, Yin-Wong & Friedman, Daniel, 1997. "Individual Learning in Normal Form Games: Some Laboratory Results," Games and Economic Behavior, Elsevier, vol. 19(1), pages 46-76, April.
    25. Eraslan, Hulya & Merlo, Antonio, 2002. "Majority Rule in a Stochastic Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 103(1), pages 31-48, March.
    26. Frechette, Guillaume R. & Kagel, John H. & Morelli, Massimo, 2005. "Gamson's Law versus non-cooperative bargaining theory," Games and Economic Behavior, Elsevier, vol. 51(2), pages 365-390, May.
    27. Brian Knight, 2002. "Endogenous Federal Grants and Crowd-out of State Government Spending: Theory and Evidence from the Federal Highway Aid Program," American Economic Review, American Economic Association, vol. 92(1), pages 71-92, March.
    28. Antonio Cabrales & Walter Garcia Fontes, 2000. "Estimating learning models from experimental data," Economics Working Papers 501, Department of Economics and Business, Universitat Pompeu Fabra.
    29. Frechette, Guillaume & Kagel, John H. & Morelli, Massimo, 2005. "Nominal bargaining power, selection protocol, and discounting in legislative bargaining," Journal of Public Economics, Elsevier, vol. 89(8), pages 1497-1517, August.
    30. Messick, David M. & Moore, Don A. & Bazerman, Max H., 1997. "Ultimatum Bargaining with a Group: Underestimating the Importance of the Decision Rule," Organizational Behavior and Human Decision Processes, Elsevier, vol. 69(2), pages 87-101, February.
    31. Teck H Ho & Colin Camerer & Juin-Kuan Chong, 2003. "Functional EWA: A one-parameter theory of learning in games," Levine's Working Paper Archive 506439000000000514, David K. Levine.
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    2. Mallucci, Paola & Wu, Diana Yan & Cui, Tony Haitao, 2019. "Social motives in bilateral bargaining games: How power changes perceptions of fairness," Journal of Economic Behavior & Organization, Elsevier, vol. 166(C), pages 138-152.
    3. Nunnari, Salvatore & Zapal, Jan, 2016. "Gambler's fallacy and imperfect best response in legislative bargaining," Games and Economic Behavior, Elsevier, vol. 99(C), pages 275-294.
    4. Olivier Armantier, 2006. "Do Wealth Differences Affect Fairness Considerations?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 391-429, May.
    5. John C. Ham & Steven F. Lehrer, 0. "Instrumental variables estimation of a simple dynamic model of bidding behavior in private value auctions," Journal of the Economic Science Association, Springer;Economic Science Association, vol. 0, pages 1-17.
    6. Breitmoser, Yves & Tan, Jonathan H.W., 2010. "Generosity in bargaining: Fair or fear?," MPRA Paper 27444, University Library of Munich, Germany.
    7. Maaser, Nicola & Traub, Stefan & Paetzel, Fabian, 2017. "Power illusion in coalitional bargaining: An experimental analysis," VfS Annual Conference 2017 (Vienna): Alternative Structures for Money and Banking 168155, Verein für Socialpolitik / German Economic Association.
    8. John C. Ham & Steven F. Lehrer, 2020. "Instrumental variables estimation of a simple dynamic model of bidding behavior in private value auctions," Journal of the Economic Science Association, Springer;Economic Science Association, vol. 6(2), pages 139-155, December.

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