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Recombinant estimation for normal-form games, with applications to auctions and bargaining

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  • Mullin, Charles H.
  • Reiley, David H.

Abstract

In empirical analysis of economic games, researchers frequently wish to estimate quantities describing group outcomes, such as the expected revenue in an auction or the mean allocative efficiency in a market experiment. For such applications, we propose an improved statistical estimation technique called "recombinant estimation." The technique takes observations of the complete strategy of each player and recombines them to compute all the possible group outcomes which could have resulted from different matches of players. We calculate the improvement in efficiency of the recombinant estimator relative to the standard estimator, and show how to estimate standard errors for the recombinant estimator for use in hypothesis testing. We present an application to a two-player sealed-bid auction and a two-player ultimatum bargaining game. In these applications, the improved efficiency of our estimator is equivalent to an increase of between 40% and 200% in the sample size. We discuss how to design game experiments in order to be able to take full advantage of recombinant estimation. Finally, we discuss practical computational issues, showing how one can avoid combinatorial explosions of computing time while still yielding significantly improved efficiency of estimation.
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Suggested Citation

  • Mullin, Charles H. & Reiley, David H., 2006. "Recombinant estimation for normal-form games, with applications to auctions and bargaining," Games and Economic Behavior, Elsevier, vol. 54(1), pages 159-182, January.
  • Handle: RePEc:eee:gamebe:v:54:y:2006:i:1:p:159-182
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    References listed on IDEAS

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    1. Mitzkewitz, Michael & Nagel, Rosemarie, 1993. "Experimental Results on Ultimatum Games with Incomplete Information," International Journal of Game Theory, Springer;Game Theory Society, vol. 22(2), pages 171-198.
    2. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
    3. Robert Moir, 1998. "A Monte Carlo Analysis of the Fisher Randomization Technique: Reviving Randomization for Experimental Economists," Experimental Economics, Springer;Economic Science Association, vol. 1(1), pages 87-100, June.
    4. Mehta, Judith & Starmer, Chris & Sugden, Robert, 1994. "The Nature of Salience: An Experimental Investigation of Pure Coordination Games," American Economic Review, American Economic Association, vol. 84(3), pages 658-673, June.
    5. David Lucking-Reiley & John A. List, 2000. "Demand Reduction in Multiunit Auctions: Evidence from a Sportscard Field Experiment," American Economic Review, American Economic Association, vol. 90(4), pages 961-972, September.
    6. Kagel, John H & Harstad, Ronald M & Levin, Dan, 1987. "Information Impact and Allocation Rules in Auctions with Affiliated Private Values: A Laboratory Study," Econometrica, Econometric Society, vol. 55(6), pages 1275-1304, November.
    7. Kagel, John H & Levin, Dan, 1993. "Independent Private Value Auctions: Bidder Behaviour in First-, Second- and Third-Price Auctions with Varying Numbers of Bidders," Economic Journal, Royal Economic Society, vol. 103(419), pages 868-879, July.
    8. Friedman, Daniel, 1996. "Equilibrium in Evolutionary Games: Some Experimental Results," Economic Journal, Royal Economic Society, vol. 106(434), pages 1-25, January.
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    Cited by:

    1. Pintér, Ágnes & Veszteg, Róbert F., 2010. "Minority vs. majority: An experimental study of standardized bids," European Journal of Political Economy, Elsevier, vol. 26(1), pages 36-50, March.
    2. repec:eee:ecolet:v:164:y:2018:i:c:p:75-78 is not listed on IDEAS
    3. Rodney Garratt & Mark Walker & John Wooders, 2012. "Behavior in second-price auctions by highly experienced eBay buyers and sellers," Experimental Economics, Springer;Economic Science Association, vol. 15(1), pages 44-57, March.
    4. repec:jmi:articl:jmi-v1i1a2 is not listed on IDEAS
    5. Calsamiglia, Caterina & Haeringer, Guillaume & Klijn, Flip, 2011. "A comment on "School choice: An experimental study" [J. Econ. Theory 127 (1) (2006) 202-231]," Journal of Economic Theory, Elsevier, vol. 146(1), pages 392-396, January.
    6. López-Pérez, Raúl & Pintér, Ágnes & Kiss, Hubert J., 2015. "Does payoff equity facilitate coordination? A test of Schelling's conjecture," Journal of Economic Behavior & Organization, Elsevier, vol. 117(C), pages 209-222.
    7. Bergstrom, Carl T. & Bergstrom, Ted C & Garratt, Rod, 2009. "Ideal Bootstrapping and Exact Recombination: Applications to Auction Experiments," University of California at Santa Barbara, Economics Working Paper Series qt4xb7454q, Department of Economics, UC Santa Barbara.
    8. Yan Chen & Sherry Xin Li, 2009. "Group Identity and Social Preferences," American Economic Review, American Economic Association, vol. 99(1), pages 431-457, March.
    9. Jason Abrevaya, 2008. "On recombinant estimation for experimental data," Experimental Economics, Springer;Economic Science Association, vol. 11(1), pages 25-52, March.

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