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Equilibrium Selection in Sequential Games with Imperfect Information

Author

Listed:
  • Jon X. Eguia

    (Department of Economics, Univ. of Bristol. and Department of Politics, New York Univ.)

  • Aniol Llorente-Saguer

    (School of Economics and Finance, Queen Mary, Univ. of London)

  • Rebecca Morton

    (Department of Politics, NYU-NYC and NYU-Abu Dhabi.)

  • Antonio Nicolò

    (School of Social Sciences, Univ. of Manchester)

Abstract

Games with imperfect information often feature multiple equilibria, which depend on beliefs off the equilibrium path. Standard selection criteria such as passive beliefs, symmetric beliefs or wary beliefs rest on ad hoc restrictions on beliefs. We propose a new selection criterion that imposes no restrictions on beliefs: we select the action profi?le that is supported in equilibrium by the largest set of beliefs. We conduct experiments to test the predictive power of the existing and our novel selection criteria in two applications: a game of vertical multi-lateral contracting, and a game of electoral competition. We fi?nd that our selection criterion outperforms the other selection criteria.

Suggested Citation

  • Jon X. Eguia & Aniol Llorente-Saguer & Rebecca Morton & Antonio Nicolò, 2014. "Equilibrium Selection in Sequential Games with Imperfect Information," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2014_04, Max Planck Institute for Research on Collective Goods.
    • Handle: RePEc:mpg:wpaper:2014_04
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    1. Eguia, Jon X. & Llorente-Saguer, Aniol & Morton, Rebecca & Nicolò, Antonio, 2018. "Equilibrium selection in sequential games with imperfect information," Games and Economic Behavior, Elsevier, vol. 109(C), pages 465-483.
    2. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, December.
    3. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    4. Marco Pagnozzi & Salvatore Piccolo, 2012. "Vertical Separation with Private Contracts," Economic Journal, Royal Economic Society, vol. 122(559), pages 173-207, March.
    5. Nocke, Volker & Rey, Patrick, 2018. "Exclusive dealing and vertical integration in interlocking relationships," Journal of Economic Theory, Elsevier, vol. 177(C), pages 183-221.
    6. Peski, Marcin, 2010. "Generalized risk-dominance and asymmetric dynamics," Journal of Economic Theory, Elsevier, vol. 145(1), pages 216-248, January.
    7. Oliver Hart & Jean Tirole, 1990. "Vertical Integration and Market Foreclosure," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 21(1990 Micr), pages 205-286.
    8. Jan Boone & Wieland Müller & Sigrid Suetens, 2014. "Naked Exclusion in the Lab: The Case of Sequential Contracting," Journal of Industrial Economics, Wiley Blackwell, vol. 62(1), pages 137-166, March.
    9. Harsanyi John C., 1995. "A New Theory of Equilibrium Selection for Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 10(2), pages 318-332, August.
    10. Heski Bar-Isaac & Guillermo Caruana & Vicente Cunat, 2012. "Search, Design, and Market Structure," American Economic Review, American Economic Association, vol. 102(2), pages 1140-1160, April.
    11. Jon X. Eguia & Antonio Nicolò, 2011. "On the Efficiency of Partial Information in Elections," Carlo Alberto Notebooks 234, Collegio Carlo Alberto.
    12. Eric Avenel, 2012. "Upstream Capacity Constraint and the Preservation of Monopoly Power in Private Bilateral Contracting," Journal of Industrial Economics, Wiley Blackwell, vol. 60(4), pages 578-598, December.
    13. Jeanine Miklós-Thal & Greg Shaffer, 2016. "Naked Exclusion with Private Offers," American Economic Journal: Microeconomics, American Economic Association, vol. 8(4), pages 174-194, November.
    14. Schmidt, David & Shupp, Robert & Walker, James M. & Ostrom, Elinor, 2003. "Playing safe in coordination games:: the roles of risk dominance, payoff dominance, and history of play," Games and Economic Behavior, Elsevier, vol. 42(2), pages 281-299, February.
    15. 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.
    16. Srihari Govindan & Robert Wilson, 2009. "On Forward Induction," Econometrica, Econometric Society, vol. 77(1), pages 1-28, January.
    17. Stéphane Caprice & Patrick Rey, 2015. "Buyer Power from Joint Listing Decision," Economic Journal, Royal Economic Society, vol. 125(589), pages 1677-1704, December.
    18. Cabrales, Antonio & Garcia-Fontes, Walter & Motta, Massimo, 2000. "Risk dominance selects the leader: An experimental analysis," International Journal of Industrial Organization, Elsevier, vol. 18(1), pages 137-162, January.
    19. Alessandro Gavazza & Alessandro Lizzeri, 2009. "Transparency and Economic Policy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(3), pages 1023-1048.
    20. In-Koo Cho & David M. Kreps, 1987. "Signaling Games and Stable Equilibria," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 102(2), pages 179-221.
    21. Catherine C. de Fontenay & Joshua S. Gans, 2005. "Vertical Integration in the Presence of Upstream Competition," RAND Journal of Economics, The RAND Corporation, vol. 36(3), pages 544-572, Autumn.
    22. Buehler, Benno & Schuett, Florian, 2014. "Certification and minimum quality standards when some consumers are uninformed," European Economic Review, Elsevier, vol. 70(C), pages 493-511.
    23. Younghwan In & Julian Wright, 2018. "Signaling Private Choices," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(1), pages 558-580.
    24. Catherine C. Fontenay & Joshua S. Gans, 2014. "Bilateral Bargaining with Externalities," Journal of Industrial Economics, Wiley Blackwell, vol. 62(4), pages 756-788, December.
    25. Banks, Jeffrey S & Sobel, Joel, 1987. "Equilibrium Selection in Signaling Games," Econometrica, Econometric Society, vol. 55(3), pages 647-661, May.
    26. Patrick Rey & Thibaud Vergé, 2004. "Bilateral Control with Vertical Contracts," RAND Journal of Economics, The RAND Corporation, vol. 35(4), pages 728-746, Winter.
    27. Katherine Ho, 2009. "Insurer-Provider Networks in the Medical Care Market," American Economic Review, American Economic Association, vol. 99(1), pages 393-430, March.
    28. Eric Avenel, 2012. "Suppliers’ Merger and Consumers' Welfare," Ekonomia, Cyprus Economic Society and University of Cyprus, vol. 15(1), pages 1-21, Summer.
    29. Moellers, Claudia & Normann, Hans-Theo & Snyder, Christopher M., 2017. "Communication in vertical markets: Experimental evidence," International Journal of Industrial Organization, Elsevier, vol. 50(C), pages 214-258.
    30. 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.
    31. Daniel P. O'Brien & Greg Shaffer, 1992. "Vertical Control with Bilateral Contracts," RAND Journal of Economics, The RAND Corporation, vol. 23(3), pages 299-308, Autumn.
    32. Markus Reisinger & Emanuele Tarantino, 2015. "Vertical integration, foreclosure, and productive efficiency," RAND Journal of Economics, RAND Corporation, vol. 46(3), pages 461-479, September.
    33. Swati Dhingra & Andrew Bernard, 2015. "Contracting and the Division of the Gains from Trade," 2015 Meeting Papers 298, Society for Economic Dynamics.
    34. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
    35. Rey, Patrick & Tirole, Jean, 2007. "A Primer on Foreclosure," Handbook of Industrial Organization, in: Mark Armstrong & Robert Porter (ed.), Handbook of Industrial Organization, edition 1, volume 3, chapter 33, pages 2145-2220, Elsevier.
    36. Anil Arya & Brian Mittendorf, 2011. "Disclosure standards for vertical contracts," RAND Journal of Economics, RAND Corporation, vol. 42(3), pages 595-617, September.
    37. Croson, Rachel T. A., 2000. "Thinking like a game theorist: factors affecting the frequency of equilibrium play," Journal of Economic Behavior & Organization, Elsevier, vol. 41(3), pages 299-314, March.
    38. Hagiu, Andrei & Hałaburda, Hanna, 2014. "Information and two-sided platform profits," International Journal of Industrial Organization, Elsevier, vol. 34(C), pages 25-35.
    39. Markus K. Brunnermeier & Martin Oehmke, 2013. "The Maturity Rat Race," Journal of Finance, American Finance Association, vol. 68(2), pages 483-521, April.
    40. Ilya Segal, 1999. "Contracting with Externalities," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(2), pages 337-388.
    41. Stéphane Caprice, 2006. "Multilateral Vertical Contracting with an Alternative Supply: The Welfare Effects of a Ban on Price Discrimination," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 28(1), pages 63-80, February.
    42. Roman Inderst & Marco Ottaviani, 2012. "Competition through Commissions and Kickbacks," American Economic Review, American Economic Association, vol. 102(2), pages 780-809, April.
    43. Jan Boone & Wieland Müller & Sigrid Suetens, 2014. "Naked Exclusion in the Lab: The Case of Sequential Contracting," Journal of Industrial Economics, Wiley Blackwell, vol. 62(1), pages 137-166, March.
    44. Greiner, Ben, 2004. "An Online Recruitment System for Economic Experiments," MPRA Paper 13513, University Library of Munich, Germany.
    45. Selten, Reinhard, 1995. "An axiomatic theory of a risk dominance measure for bipolar games with linear incentives," Games and Economic Behavior, Elsevier, vol. 8(1), pages 213-263.
    46. Martin, Stephen & Normann, Hans-Theo & Snyder, Christopher M, 2001. "Vertical Foreclosure in Experimental Markets," RAND Journal of Economics, The RAND Corporation, vol. 32(3), pages 466-496, Autumn.
    47. McAfee, R Preston & Schwartz, Marius, 1994. "Opportunism in Multilateral Vertical Contracting: Nondiscrimination, Exclusivity, and Uniformity," American Economic Review, American Economic Association, vol. 84(1), pages 210-230, March.
    48. Dina Mayzlin & Hema Yoganarasimhan, 2012. "Link to Success: How Blogs Build an Audience by Promoting Rivals," Management Science, INFORMS, vol. 58(9), pages 1651-1668, September.
    49. Ilya Segal & Michael D. Whinston, 2003. "Robust Predictions for Bilateral Contracting with Externalities," Econometrica, Econometric Society, vol. 71(3), pages 757-791, May.
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    Cited by:

    1. Janssen, Maarten C.W., 2020. "Vertical contracts in search markets," International Journal of Industrial Organization, Elsevier, vol. 70(C).
    2. Moellers, Claudia & Normann, Hans-Theo & Snyder, Christopher M., 2017. "Communication in vertical markets: Experimental evidence," International Journal of Industrial Organization, Elsevier, vol. 50(C), pages 214-258.
    3. Eguia, Jon X. & Llorente-Saguer, Aniol & Morton, Rebecca & Nicolò, Antonio, 2018. "Equilibrium selection in sequential games with imperfect information," Games and Economic Behavior, Elsevier, vol. 109(C), pages 465-483.
    4. Nicolas Pasquier & Olivier Bonroy & Alexis Garapin, 2022. "Risk aversion and equilibrium selection in a vertical contracting setting: an experiment," Theory and Decision, Springer, vol. 93(4), pages 585-614, November.
    5. Eguia, Jon X. & Nicolo, Antonio, 2019. "Information and targeted spending," Theoretical Economics, Econometric Society, vol. 14(2), May.
    6. Jeanine Miklós-Thal & Greg Shaffer, 2016. "Naked Exclusion with Private Offers," American Economic Journal: Microeconomics, American Economic Association, vol. 8(4), pages 174-194, November.
    7. Maris Goldmanis & Korok Ray, 2021. "Team incentives under private contracting," RAND Journal of Economics, RAND Corporation, vol. 52(2), pages 334-358, June.
    8. Normann, Hans-Theo & Möllers, Claudia & Snyder, Christopher M., 2015. "Communication in Vertically Related Markets: Experimental Evidence," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 112842, Verein für Socialpolitik / German Economic Association.
    9. Maria Carmela Ceparano & Jacqueline Morgan, 2017. "Equilibrium selection in multi-leader-follower games with vertical information," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 526-543, October.

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    More about this item

    Keywords

    imperfect information; equilibrium selection; passive beliefs; symmetric beliefs; vertical contract- ing; multiple equilibria;
    All these keywords.

    JEL classification:

    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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