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Computational analysis of perfect-information position auctions

Author

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  • Thompson, David R.M.
  • Leyton-Brown, Kevin

Abstract

After experimentation with other designs, major search engines converged on weighted, generalized second-price auctions (wGSPs) for selling keyword advertisements. Theoretical analysis is still not able to settle the question of why they found this design preferable to other alternatives. We approach this question in a new way, adopting an analytical paradigm we dub “computational mechanism analysis.” Specifically, we sample position auction games from a given distribution, encode them in a computationally efficient representation language, compute their Nash equilibria, and calculate economic quantities of interest. We considered seven widely studied valuation models from the literature and three position auction variants. We found that wGSP consistently showed the best ads of any position auction, measured both by social welfare and expected number of clicks. In contrast, we found that revenue was extremely variable across auction mechanisms and was highly sensitive to equilibrium selection, the preference model, and the valuation distribution.

Suggested Citation

  • Thompson, David R.M. & Leyton-Brown, Kevin, 2017. "Computational analysis of perfect-information position auctions," Games and Economic Behavior, Elsevier, vol. 102(C), pages 583-623.
  • Handle: RePEc:eee:gamebe:v:102:y:2017:i:c:p:583-623
    DOI: 10.1016/j.geb.2017.02.009
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    References listed on IDEAS

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    1. Susan Athey & Glenn Ellison, 2011. "Position Auctions with Consumer Search," The Quarterly Journal of Economics, Oxford University Press, vol. 126(3), pages 1213-1270.
    2. Benjamin Edelman & Michael Ostrovsky & Michael Schwarz, 2007. "Internet Advertising and the Generalized Second-Price Auction: Selling Billions of Dollars Worth of Keywords," American Economic Review, American Economic Association, vol. 97(1), pages 242-259, March.
    3. Talman, A.J.J. & van der Laan, G. & Van der Heyden, L., 1987. "Variable dimension algorithms for solving the nonlinear complementarity problem on a product of unit simplices using general labelling," Other publications TiSEM fbe9ae2f-e01d-4eef-944c-6, Tilburg University, School of Economics and Management.
    4. Porter, Ryan & Nudelman, Eugene & Shoham, Yoav, 2008. "Simple search methods for finding a Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 63(2), pages 642-662, July.
    5. Gomes, Renato & Sweeney, Kane, 2014. "Bayes–Nash equilibria of the generalized second-price auction," Games and Economic Behavior, Elsevier, vol. 86(C), pages 421-437.
    6. Govindan, Srihari & Wilson, Robert, 2003. "A global Newton method to compute Nash equilibria," Journal of Economic Theory, Elsevier, vol. 110(1), pages 65-86, May.
    7. Varian, Hal R., 2007. "Position auctions," International Journal of Industrial Organization, Elsevier, vol. 25(6), pages 1163-1178, December.
    8. Jiang, Albert Xin & Leyton-Brown, Kevin & Bhat, Navin A.R., 2011. "Action-Graph Games," Games and Economic Behavior, Elsevier, vol. 71(1), pages 141-173, January.
    9. G. van der Laan & A. J. J. Talman & L. van der Heyden, 1987. "Simplicial Variable Dimension Algorithms for Solving the Nonlinear Complementarity Problem on a Product of Unit Simplices Using a General Labelling," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 377-397, August.
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    More about this item

    Keywords

    Computational mechanism analysis; Position auctions; Sponsored search; Compact game representations;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design
    • L86 - Industrial Organization - - Industry Studies: Services - - - Information and Internet Services; Computer Software
    • M37 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Marketing and Advertising - - - Advertising

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