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Pure strategy equilibria of multidimensional and non-monotonic auctions

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  • Moreira, Humberto Ataíde
  • Araújo, Aloísio Pessoa de
  • Castro Filho, Luciano I. de

Abstract

We give necessary and sufficient conditions for the existence of symmetric equilibrium without ties in interdependent values auctions, with multidimensional independent types and no monotonic assumptions. In this case, non-monotonic equilibria might happen. When the necessary and sufficient conditions are not satisfied, there are ties with positive probability. In such case, we are still able to prove the existence of pure strategy equilibrium with an all-pay auction tie-breaking rule. As a direct implication of these results, we obtain a generalization of the Revenue Equivalence Theorem. From the robustness of equilibrium existence for all-pay auctions in multidimensional setting, an interpretation of our results can give a new justification to the use of tournaments in practice.

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  • Moreira, Humberto Ataíde & Araújo, Aloísio Pessoa de & Castro Filho, Luciano I. de, 2004. "Pure strategy equilibria of multidimensional and non-monotonic auctions," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 571, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  • Handle: RePEc:fgv:epgewp:571
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    as
    1. Monteiro, Paulo Klinger, 2009. "First-price auction symmetric equilibria with a general distribution," Games and Economic Behavior, Elsevier, vol. 65(1), pages 256-269, January.
    2. Veloso, Fernando A. & Ferreira, Pedro Cavalcanti & Pessôa, Samuel de Abreu, 2004. "On the tyranny of numbers: East Asian miracles in world perspective," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 569, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    3. Roger B. Myerson, 1978. "Optimal Auction Design," Discussion Papers 362, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Eric Maskin & John Riley, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 439-454.
    5. Guesnerie,Roger, 1998. "A Contribution to the Pure Theory of Taxation," Cambridge Books, Cambridge University Press, number 9780521629560, May.
    6. Jehiel, Philippe & Moldovanu, Benny & Stacchetti, Ennio, 1996. "How (Not) to Sell Nuclear Weapons," American Economic Review, American Economic Association, vol. 86(4), pages 814-829, September.
    7. Simon, Leo K & Zame, William R, 1990. "Discontinuous Games and Endogenous Sharing Rules," Econometrica, Econometric Society, vol. 58(4), pages 861-872, July.
    8. Yeon-Koo Che, 1993. "Design Competition through Multidimensional Auctions," RAND Journal of Economics, The RAND Corporation, vol. 24(4), pages 668-680, Winter.
    9. Harsanyi, John C, 1995. "Games with Incomplete Information," American Economic Review, American Economic Association, vol. 85(3), pages 291-303, June.
    10. Martimort, David & Moreira, Humberto Ataíde, 2004. "Common agency with informed principals," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 551, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    11. Susan Athey & Jonathan Levin, 2001. "Information and Competition in U.S. Forest Service Timber Auctions," Journal of Political Economy, University of Chicago Press, vol. 109(2), pages 375-417, April.
    12. Border, Kim C, 1991. "Implementation of Reduced Form Auctions: A Geometric Approach," Econometrica, Econometric Society, vol. 59(4), pages 1175-1187, July.
    13. Cysne, Rubens Penha, 2004. "On the Statistical Estimation of Diffusion Processes: A Partial Survey," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 24(2), November.
    14. Xiao, Zhijie & Lima, Luiz Renato Regis de Oliveira, 2004. "Purchasing power parity and the unit root tests: a robust analysis," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 552, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    15. Araujo, Aloisio & Moreira, Humberto, 2010. "Adverse selection problems without the Spence-Mirrlees condition," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1113-1141, May.
    16. Zheng, Charles Z., 2001. "High Bids and Broke Winners," Journal of Economic Theory, Elsevier, vol. 100(1), pages 129-171, September.
    17. Riley, John G & Samuelson, William F, 1981. "Optimal Auctions," American Economic Review, American Economic Association, vol. 71(3), pages 381-392, June.
    18. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    19. Perez, Leonardo Pio & Ferreira, Pedro Cavalcanti, 2004. "Efeitos macroeconômicos e custos sociais de uma transição entre regimes de previdência no Brasil," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 556, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    20. Laffont, Jean-Jacques, 1997. "Game theory and empirical economics: The case of auction data 1," European Economic Review, Elsevier, vol. 41(1), pages 1-35, January.
    21. Cysne, Rubens Penha, 2004. "Income inequality: the role of impatience in a job-search process," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 559, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    22. repec:wsi:wschap:9789814374590_0009 is not listed on IDEAS
    23. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2003. "Rationalizable bidding in first-price auctions," Games and Economic Behavior, Elsevier, vol. 45(1), pages 38-72, October.
    24. Cavalcanti, Ricardo de Oliveira & Forno, Henrique Dezemone, 2004. "Cyclical Interest Payments on Inside Money," Economics Working Papers (Ensaios Economicos da EPGE) 546, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    25. Lizzeri, Alessandro & Persico, Nicola, 2000. "Uniqueness and Existence of Equilibrium in Auctions with a Reserve Price," Games and Economic Behavior, Elsevier, vol. 30(1), pages 83-114, January.
    26. Cavalcanti, Ricardo de Oliveira & Forno, Henrique Dezemone, 2004. "Money with Bank Networks," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 545, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    27. Cysne, Rubens Penha, 2004. "A search-theoretic explanation for the negative correlation between labor income and impatience," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 558, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    28. Philip J. Reny & Shmuel Zamir, 2004. "On the Existence of Pure Strategy Monotone Equilibria in Asymmetric First-Price Auctions," Econometrica, Econometric Society, vol. 72(4), pages 1105-1125, July.
    29. Rubens Penha Cysne, 2009. "On the Positive Correlation between Income Inequality and Unemployment," The Review of Economics and Statistics, MIT Press, vol. 91(1), pages 218-226, February.
    30. Neri, Marcelo Cortes & Xerez, Marcelo, 2003. "Desenho de um sistema de metas sociais," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 519, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    31. Cysne, Rubens Penha, 2004. "Inflation and income inequality: A link through the job-search process," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 557, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    32. Taylor, Curtis R, 1995. "Digging for Golden Carrots: An Analysis of Research Tournaments," American Economic Review, American Economic Association, vol. 85(4), pages 872-890, September.
    33. Matthew O. Jackson & Leo K. Simon & Jeroen M. Swinkels & William R. Zame, 2002. "Communication and Equilibrium in Discontinuous Games of Incomplete Information," Econometrica, Econometric Society, vol. 70(5), pages 1711-1740, September.
    34. Aloisio Araujo & Humberto Moreira, 2001. "Non-monotone insurance contracts and their empirical consequences," Textos para discussão 449, Department of Economics PUC-Rio (Brazil).
    35. Hanming Fang & Stephen Morris, 2012. "Multidimensional Private Value Auctions," World Scientific Book Chapters,in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 9, pages 319-356 World Scientific Publishing Co. Pte. Ltd..
    36. Cysne, Rubens Penha, 2004. "Solving the non-convexity problem in some shopping-time and human-capital models," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 567, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    37. Maskin, Eric S & Riley, John G, 1984. "Optimal Auctions with Risk Averse Buyers," Econometrica, Econometric Society, vol. 52(6), pages 1473-1518, November.
    38. David McAdams, 2003. "Isotone Equilibrium in Games of Incomplete Information," Econometrica, Econometric Society, vol. 71(4), pages 1191-1214, July.
    39. Daniel Gottlieb & Lucas Maestri, 2004. "Banning Information As A Redistributive Device," Anais do XXXII Encontro Nacional de Economia [Proceedings of the 32nd Brazilian Economics Meeting] 046, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    40. Ewerhart, Christian & Fieseler, Karsten, 2003. " Procurement Auctions and Unit-Price Contracts," RAND Journal of Economics, The RAND Corporation, vol. 34(3), pages 569-581, Autumn.
    41. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    42. Cysne, Rubens Penha, 2004. "On the statistical estimation of diffusion processes: a survey," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 540, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    43. Philippe Jehiel & Moritz Meyer-ter-Vehn & Benny Moldovanu & William R. Zame, 2006. "The Limits of ex post Implementation," Econometrica, Econometric Society, vol. 74(3), pages 585-610, May.
    44. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
    45. Barbosa, Fernando de Holanda, 2004. "Dois experimentos de política monetária no modelo novo-keynesiano," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 547, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    46. Matthew O. Jackson & Leo K. Simon & Jeroen M. Swinkels & William R. Zame, 2004. "Corrigendum to "Communication and Equilibrium in Discontinuous Games of Incomplete Information"," Econometrica, Econometric Society, vol. 72(6), pages 1927-1929, November.
    47. Steven R. Williams, 1991. "Existence and Convergence of Equilibria in the Buyer's Bid Double Auction," Review of Economic Studies, Oxford University Press, vol. 58(2), pages 351-374.
    48. Cysne, Rubens Penha & Maldonado, Wilfredo Fernando Leiva & Monteiro, P. K., 2004. "Inflation and income inequality: a shopping-time aproach: (Forthcoming, Journal of Development Economics)," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 566, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    49. Matthews, Steven A, 1984. "On the Implementability of Reduced Form Auctions," Econometrica, Econometric Society, vol. 52(6), pages 1519-1522, November.
    50. Partha Dasgupta & Eric Maskin, 2000. "Efficient Auctions," The Quarterly Journal of Economics, Oxford University Press, vol. 115(2), pages 341-388.
    51. Guesnerie, Roger & Laffont, Jean-Jacques, 1984. "A complete solution to a class of principal-agent problems with an application to the control of a self-managed firm," Journal of Public Economics, Elsevier, vol. 25(3), pages 329-369, December.
    52. Aloisio Araujo & Luciano I. de Castro Filho, 2004. "Pure Strategy Equilibria of Multidimensional and Non-Monotonic Auctions," Econometric Society 2004 Latin American Meetings 300, Econometric Society.
    53. Cysne, Rubens Penha, 2004. "A general-equilibrium closed-form solution to the welfare costs of inflation (Forthcoming, Revista Brasileira de Economia)," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 562, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    54. Gottlieb, Daniel & Moreira, Humberto Ataíde & Araújo, Aloísio Pessoa de, 2004. "A model of mixed signals with applications to countersignaling an the GED," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 553, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    55. Krishna, Vijay & Morgan, John, 1997. "An Analysis of the War of Attrition and the All-Pay Auction," Journal of Economic Theory, Elsevier, vol. 72(2), pages 343-362, February.
    56. Athey, Susan, 2001. "Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Econometrica, Econometric Society, vol. 69(4), pages 861-889, July.
    57. Cysne, Rubens P. & Maldonado, Wilfredo L. & Monteiro, Paulo Klinger, 2005. "Inflation and income inequality: A shopping-time approach," Journal of Development Economics, Elsevier, vol. 78(2), pages 516-528, December.
    58. Chen, Yu-Min, 1986. "An Extension to the Implementability of Reduced Form Auctions," Econometrica, Econometric Society, vol. 54(5), pages 1249-1251, September.
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    Cited by:

    1. Athayde, Gustavo M. de & Flôres Junior, Renato Galvão, 2004. "Do higher moments really matter in portfolio choice?," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 574, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    2. Matthew Jackson, 2009. "Non-existence of equilibrium in Vickrey, second-price, and English auctions," Review of Economic Design, Springer;Society for Economic Design, vol. 13(1), pages 137-145, April.
    3. Araújo, Fabio & Issler, João Victor & Fernandes, Marcelo, 2005. "Estimating the stochastic discount factor without a utility function," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 583, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    4. Barbosa, Fernando de Holanda, 2005. "The contagion effect of public debt on monetary policy: the brazilian experience," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 591, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    5. Aloisio Araujo & Luciano Castro & Humberto Moreira, 2008. "Non-monotoniticies and the all-pay auction tie-breaking rule," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(3), pages 407-440, June.
    6. Moreira, Humberto Ataíde & Araújo, Aloísio Pessoa de & Castro Filho, Luciano I. de, 2004. "Pure strategy equilibria of multidimensional and non-monotonic auctions," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 571, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    7. Fernando Barbosa & Alexandre Cunha & Elvia Sallum, 2006. "Competitive equilibrium hyperinflation under rational expectations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 181-195, September.
    8. Araujo, Aloisio & de Castro, Luciano I., 2009. "Pure strategy equilibria of single and double auctions with interdependent values," Games and Economic Behavior, Elsevier, vol. 65(1), pages 25-48, January.
    9. Horowitz, Andrew W. & Flôres Junior, Renato Galvão, 2004. "Beyond indifferent players: on the existence of prisoners dilemmas in games with amicable and adversarial preferences," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 576, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).

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    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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