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Strategic complementarity in games

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  • Vives, Xavier
  • Vravosinos, Orestis

Abstract

The lattice-theoretic approach has had a significant impact in all fields of economics, being progressively incorporated into the standard toolbox. This paper presents a selective survey with an emphasis on basic tools, some important results, and applications in industrial organization, dynamic games, games of incomplete information, and mechanism design. Frontier theoretical research employing lattice-theoretic methods continues to be developed in areas such as mean-field games and information design.

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  • Vives, Xavier & Vravosinos, Orestis, 2024. "Strategic complementarity in games," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    • Handle: RePEc:eee:mateco:v:113:y:2024:i:c:s0304406824000673
    DOI: 10.1016/j.jmateco.2024.103005
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    1. Balbus, Lukasz & Reffett, Kevin & Wozny, Lukasz, 2015. "Monotone equilibria in nonatomic supermodular games. A comment," Games and Economic Behavior, Elsevier, vol. 94(C), pages 182-187.
    2. Eyal Winter, 2004. "Incentives and Discrimination," American Economic Review, American Economic Association, vol. 94(3), pages 764-773, June.
    3. Dirk Bergemann & Stephen Morris, 2019. "Information Design: A Unified Perspective," Journal of Economic Literature, American Economic Association, vol. 57(1), pages 44-95, March.
    4. José Azar & Xavier Vives, 2021. "General Equilibrium Oligopoly and Ownership Structure," Econometrica, Econometric Society, vol. 89(3), pages 999-1048, May.
    5. Jean-Charles Rochet & Xavier Vives, 2004. "Coordination Failures and the Lender of Last Resort: Was Bagehot Right After All?," Journal of the European Economic Association, MIT Press, vol. 2(6), pages 1116-1147, December.
    6. Morris, Stephen & Shin, Hyun Song, 1998. "Unique Equilibrium in a Model of Self-Fulfilling Currency Attacks," American Economic Review, American Economic Association, vol. 88(3), pages 587-597, June.
    7. Xavier Vives, 2018. "Strategic complementarities in oligopoly," Chapters, in: Luis C. Corchón & Marco A. Marini (ed.), Handbook of Game Theory and Industrial Organization, Volume I, chapter 2, pages 9-39, Edward Elgar Publishing.
    8. Daniel F. Spulber, 2013. "How Do Competitive Pressures Affect Incentives to Innovate When There Is a Market for Inventions?," Journal of Political Economy, University of Chicago Press, vol. 121(6), pages 1007-1054.
    9. Amir, Rabah & De Castro, Luciano & Koutsougeras, Leonidas, 2014. "Free entry versus socially optimal entry," Journal of Economic Theory, Elsevier, vol. 154(C), pages 112-125.
    10. Frankel, David M. & Morris, Stephen & Pauzner, Ady, 2003. "Equilibrium selection in global games with strategic complementarities," Journal of Economic Theory, Elsevier, vol. 108(1), pages 1-44, January.
    11. William Novshek, 1985. "On the Existence of Cournot Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(1), pages 85-98.
    12. Rabah Amir, 2005. "Supermodularity and Complementarity in Economics: An Elementary Survey," Southern Economic Journal, John Wiley & Sons, vol. 71(3), pages 636-660, January.
    13. Xavier Vives, 2014. "Strategic Complementarity, Fragility, and Regulation," The Review of Financial Studies, Society for Financial Studies, vol. 27(12), pages 3547-3592.
    14. Federico Echenique, 2002. "Comparative Statics by Adaptive Dynamics and the Correspondence Principle," Econometrica, Econometric Society, vol. 70(2), pages 833-844, March.
    15. John K.-H. Quah & Bruno Strulovici, 2009. "Comparative Statics, Informativeness, and the Interval Dominance Order," Econometrica, Econometric Society, vol. 77(6), pages 1949-1992, November.
    16. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
    17. Echenique, Federico, 2004. "Extensive-form games and strategic complementarities," Games and Economic Behavior, Elsevier, vol. 46(2), pages 348-364, February.
    18. Giovanni Cespa & Xavier Vives, 2015. "The Beauty Contest and Short-Term Trading," Journal of Finance, American Finance Association, vol. 70(5), pages 2099-2154, October.
    19. Rabah Amir & Val E. Lambson, 2000. "On the Effects of Entry in Cournot Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(2), pages 235-254.
    20. Jovanovic, Boyan & Rosenthal, Robert W., 1988. "Anonymous sequential games," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 77-87, February.
    21. Zhou Lin, 1994. "The Set of Nash Equilibria of a Supermodular Game Is a Complete Lattice," Games and Economic Behavior, Elsevier, vol. 7(2), pages 295-300, September.
    22. Christian Hellwig & Laura Veldkamp, 2009. "Knowing What Others Know: Coordination Motives in Information Acquisition," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(1), pages 223-251.
    23. Mensch, Jeffrey, 2020. "On the existence of monotone pure-strategy perfect Bayesian equilibrium in games with complementarities," Journal of Economic Theory, Elsevier, vol. 187(C).
    24. Feng, Yue & Sabarwal, Tarun, 2020. "Strategic complements in two stage, 2 × 2 games," Journal of Economic Theory, Elsevier, vol. 190(C).
    25. Áureo de Paula & Xun Tang, 2012. "Inference of Signs of Interaction Effects in Simultaneous Games With Incomplete Information," Econometrica, Econometric Society, vol. 80(1), pages 143-172, January.
    26. Mathevet, Laurent, 2014. "Beliefs and rationalizability in games with complementarities," Games and Economic Behavior, Elsevier, vol. 85(C), pages 252-271.
    27. Vives, Xavier & Vravosinos, Orestis, 2022. "Free entry in a Cournot market with overlapping ownership," CEPR Discussion Papers 17517, C.E.P.R. Discussion Papers.
    28. Echenique, Federico, 2004. "A characterization of strategic complementarities," Games and Economic Behavior, Elsevier, vol. 46(2), pages 325-347, February.
    29. Douglas W. Diamond & Philip H. Dybvig, 2000. "Bank runs, deposit insurance, and liquidity," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 24(Win), pages 14-23.
    30. Mary Amiti & Oleg Itskhoki & Jozef Konings, 2019. "International Shocks, Variable Markups, and Domestic Prices," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(6), pages 2356-2402.
    31. Balbus, Lukasz & Dziewulski, Pawel & Reffett, Kevin & Wozny, Lukasz, 2022. "Markov distributional equilibrium dynamics in games with complementarities and no aggregate risk," Theoretical Economics, Econometric Society, vol. 17(2), May.
    32. Xavier Vives, 2008. "Innovation And Competitive Pressure," Journal of Industrial Economics, Wiley Blackwell, vol. 56(3), pages 419-469, December.
    33. José Azar & Xavier Vives, 2021. "Reply to: Comments on “General Equilibrium Oligopoly and Ownership Structure”," Econometrica, Econometric Society, vol. 89(3), pages 1061-1063, May.
    34. Rota-Graziosi, Grégoire, 2019. "The supermodularity of the tax competition game," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 25-35.
    35. Manzano, Carolina & Vives, Xavier, 2011. "Public and private learning from prices, strategic substitutability and complementarity, and equilibrium multiplicity," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 346-369.
    36. Mas-Colell, Andreu, 1984. "On a theorem of Schmeidler," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 201-206, December.
    37. Milgrom, Paul & Roberts, John, 1994. "Comparing Equilibria," American Economic Review, American Economic Association, vol. 84(3), pages 441-459, June.
    38. Gorton, Gary, 1985. "Bank suspension of convertibility," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 177-193, March.
    39. Balbus, Łukasz & Reffett, Kevin & Woźny, Łukasz, 2014. "A constructive study of Markov equilibria in stochastic games with strategic complementarities," Journal of Economic Theory, Elsevier, vol. 150(C), pages 815-840.
    40. , A., 2010. "Supermodular mechanism design," Theoretical Economics, Econometric Society, vol. 5(3), September.
    41. Jordi Mondria & Xavier Vives & Liyan Yang, 2022. "Costly Interpretation of Asset Prices," Management Science, INFORMS, vol. 68(1), pages 52-74, January.
    42. Chen, Qi & Goldstein, Itay & Jiang, Wei, 2010. "Payoff complementarities and financial fragility: Evidence from mutual fund outflows," Journal of Financial Economics, Elsevier, vol. 97(2), pages 239-262, August.
    43. Kukushkin, Nikolai S., 1994. "A fixed-point theorem for decreasing mappings," Economics Letters, Elsevier, vol. 46(1), pages 23-26, September.
    44. Marina Halac & Ilan Kremer & Eyal Winter, 2020. "Raising Capital from Heterogeneous Investors," American Economic Review, American Economic Association, vol. 110(3), pages 889-921, March.
    45. Roberts, John & Sonnenschein, Hugo, 1976. "On the existence of Cournot equilbrium without concave profit functions," Journal of Economic Theory, Elsevier, vol. 13(1), pages 112-117, August.
    46. Fernando Alvarez & Francesco Lippi & Panagiotis Souganidis, 2023. "Price Setting With Strategic Complementarities as a Mean Field Game," Econometrica, Econometric Society, vol. 91(6), pages 2005-2039, November.
    47. Federico Echenique & Ivana Komunjer, 2009. "Testing Models With Multiple Equilibria by Quantile Methods," Econometrica, Econometric Society, vol. 77(4), pages 1281-1297, July.
    48. Acemoglu, Daron & Jensen, Martin Kaae, 2013. "Aggregate comparative statics," Games and Economic Behavior, Elsevier, vol. 81(C), pages 27-49.
    49. Yang, Jian & Qi, Xiangtong, 2013. "The nonatomic supermodular game," Games and Economic Behavior, Elsevier, vol. 82(C), pages 609-620.
    50. Anne-Christine Barthel & Eric Hoffmann, 2019. "Rationalizability and learning in games with strategic heterogeneity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(3), pages 565-587, April.
    51. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    52. Marina Halac & Elliot Lipnowski & Daniel Rappoport, 2021. "Rank Uncertainty in Organizations," American Economic Review, American Economic Association, vol. 111(3), pages 757-786, March.
    53. SCHMEIDLER, David, 1973. "Equilibrium points of nonatomic games," LIDAM Reprints CORE 146, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    54. Yeon-Koo Che & Jinwoo Kim & Fuhito Kojima, 2019. "Weak Monotone Comparative Statics," Papers 1911.06442, arXiv.org, revised Nov 2021.
    55. Echenique, Federico & Edlin, Aaron, 2004. "Mixed equilibria are unstable in games of strategic complements," Journal of Economic Theory, Elsevier, vol. 118(1), pages 61-79, September.
    56. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, vol. 65(6), pages 1283-1310, November.
    57. David McAdams, 2003. "Isotone Equilibrium in Games of Incomplete Information," Econometrica, Econometric Society, vol. 71(4), pages 1191-1214, July.
    58. Jayant Vivek Ganguli & Liyan Yang, 2009. "Complementarities, Multiplicity, and Supply Information," Journal of the European Economic Association, MIT Press, vol. 7(1), pages 90-115, March.
    59. David McAdams, 2006. "Monotone Equilibrium in Multi-Unit Auctions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(4), pages 1039-1056.
    60. Andrew Hertzberg & José María Liberti & Daniel Paravisini, 2011. "Public Information and Coordination: Evidence from a Credit Registry Expansion," Journal of Finance, American Finance Association, vol. 66(2), pages 379-412, April.
    61. Hiroto Sato, 2023. "Robust implementation in sequential information design under supermodular payoffs and objective," Review of Economic Design, Springer;Society for Economic Design, vol. 27(2), pages 269-285, June.
    62. Daron Acemoglu & Matthew O. Jackson, 2015. "History, Expectations, and Leadership in the Evolution of Social Norms," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(2), pages 423-456.
    63. Sobel, Joel, 2019. "Iterated weak dominance and interval-dominance supermodular games," Theoretical Economics, Econometric Society, vol. 14(1), January.
    64. Laurent Mathevet & Jacopo Perego & Ina Taneva, 2020. "On Information Design in Games," Journal of Political Economy, University of Chicago Press, vol. 128(4), pages 1370-1404.
    65. Maryam Farboodi & Laura Veldkamp, 2020. "Long-Run Growth of Financial Data Technology," American Economic Review, American Economic Association, vol. 110(8), pages 2485-2523, August.
    66. Bamon, Rodrigo & Fraysse, Jean, 1985. "Existence of Cournot Equilibrium in Large Markets," Econometrica, Econometric Society, vol. 53(3), pages 587-597, May.
    67. N. Gregory Mankiw & Michael D. Whinston, 1986. "Free Entry and Social Inefficiency," RAND Journal of Economics, The RAND Corporation, vol. 17(1), pages 48-58, Spring.
    68. Xavier Vives, 2009. "Strategic complementarity in multi-stage games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(1), pages 151-171, July.
    69. Yue Feng & Tarun Sabarwal, 2020. "Dynamic strategic complements in two stage, 2x2 games," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202006, University of Kansas, Department of Economics.
    70. Ilya Segal, 1999. "Contracting with Externalities," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(2), pages 337-388.
    71. Gama, Adriana & Rietzke, David, 2019. "Monotone comparative statics in games with non-monotonic best-replies: Contests and Cournot oligopoly," Journal of Economic Theory, Elsevier, vol. 183(C), pages 823-841.
    72. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    73. Daisuke Oyama & Satoru Takahashi, 2020. "Generalized Belief Operator and Robustness in Binary‐Action Supermodular Games," Econometrica, Econometric Society, vol. 88(2), pages 693-726, March.
    74. Segal, Ilya, 2003. "Coordination and discrimination in contracting with externalities: divide and conquer?," Journal of Economic Theory, Elsevier, vol. 113(2), pages 147-181, December.
    75. Brendan Kline, 2016. "The empirical content of games with bounded regressors," Quantitative Economics, Econometric Society, vol. 7(1), pages 37-81, March.
    76. Vives, Xavier, 1988. "Aggregation of Information in Large Cournot Markets," Econometrica, Econometric Society, vol. 56(4), pages 851-876, July.
    77. Curtat, Laurent O., 1996. "Markov Equilibria of Stochastic Games with Complementarities," Games and Economic Behavior, Elsevier, vol. 17(2), pages 177-199, December.
    78. 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.
    79. Donald M. Topkis, 1978. "Minimizing a Submodular Function on a Lattice," Operations Research, INFORMS, vol. 26(2), pages 305-321, April.
    80. Jun, Byoung & Vives, Xavier, 2004. "Strategic incentives in dynamic duopoly," Journal of Economic Theory, Elsevier, vol. 116(2), pages 249-281, June.
    81. Rabah Amir, 2018. "On the Cournot and Bertrand oligopolies and the theory of supermodular games," Chapters, in: Luis C. Corchón & Marco A. Marini (ed.), Handbook of Game Theory and Industrial Organization, Volume I, chapter 3, pages 40-65, Edward Elgar Publishing.
    82. Cai, Zhifeng, 2019. "Dynamic information acquisition and time-varying uncertainty," Journal of Economic Theory, Elsevier, vol. 184(C).
    83. Sachin Adlakha & Ramesh Johari, 2013. "Mean Field Equilibrium in Dynamic Games with Strategic Complementarities," Operations Research, INFORMS, vol. 61(4), pages 971-989, August.
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    More about this item

    Keywords

    Supermodular games; Strategic complementarities; Monotone comparative statics; Equilibrium comparison;
    All these keywords.

    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
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles

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