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On Strategic Complementarities in Discontinuous Games with Totally Ordered Strategies

Author

Listed:
  • Pavlo Prokopovych

    (Kyiv School of Economics)

  • Nicholas C. Yannelis

    (University of Iowa)

Abstract
This paper studies the existence of a pure strategy Nash equilibrium in games with strategic complementarities where the strategy sets are totally ordered. By relaxing the conventional conditions related to upper semicontinuity and single crossing, we enlarge the class of games to which monotone techniques are applicable. The results are illustrated with a number of economics-related examples.

Suggested Citation

  • Pavlo Prokopovych & Nicholas C. Yannelis, 2015. "On Strategic Complementarities in Discontinuous Games with Totally Ordered Strategies," Discussion Papers 56, Kyiv School of Economics.
    • Handle: RePEc:kse:dpaper:56
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    File URL: http://repec.kse.org.ua/pdf/KSE_dp56.pdf
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    References listed on IDEAS

    as
    1. Paulo Barelli & Idione Meneghel, 2013. "A Note on the Equilibrium Existence Problem in Discontinuous Games," Econometrica, Econometric Society, vol. 81(2), pages 813-824, March.
    2. 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.
    3. Aaron S. Edlin & Chris Shannon, 1998. "Strict Single Crossing and the Strict Spence-Mirrlees Condition: A Comment on Monotone Comparative Statics," Econometrica, Econometric Society, vol. 66(6), pages 1417-1426, November.
    4. Rabah Amir, 2005. "Supermodularity and Complementarity in Economics: An Elementary Survey," Southern Economic Journal, John Wiley & Sons, vol. 71(3), pages 636-660, January.
    5. Philip J. Reny, 2011. "On the Existence of Monotone Pure‐Strategy Equilibria in Bayesian Games," Econometrica, Econometric Society, vol. 79(2), pages 499-553, March.
    6. Prokopovych, Pavlo & Yannelis, Nicholas C., 2014. "On the existence of mixed strategy Nash equilibria," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 87-97.
    7. Shannon, Chris, 1995. "Weak and Strong Monotone Comparative Statics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 209-227, March.
    8. Philip J. Reny, 2020. "Nash Equilibrium in Discontinuous Games," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 439-470, August.
    9. Tian, Guoqiang & Zhou, Jianxin, 1995. "Transfer continuities, generalizations of the Weierstrass and maximum theorems: A full characterization," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 281-303.
    10. John K.‐H. Quah & Bruno Strulovici, 2012. "Aggregating the Single Crossing Property," Econometrica, Econometric Society, vol. 80(5), pages 2333-2348, September.
    11. Pavlo Prokopovych, 2011. "On equilibrium existence in payoff secure games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(1), pages 5-16, September.
    12. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    13. 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.
    14. 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.
    15. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    16. Monteiro, Paulo Klinger & Page Jr, Frank H., 2007. "Uniform payoff security and Nash equilibrium in compact games," Journal of Economic Theory, Elsevier, vol. 134(1), pages 566-575, May.
    17. Andrew McLennan & Paulo K. Monteiro & Rabee Tourky, 2011. "Games With Discontinuous Payoffs: A Strengthening of Reny's Existence Theorem," Econometrica, Econometric Society, vol. 79(5), pages 1643-1664, September.
    18. Guilherme Carmona & Konrad Podczeck, 2016. "Existence of Nash equilibrium in ordinal games with discontinuous preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 457-478, March.
    19. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521536721, September.
    20. Allison, Blake A. & Lepore, Jason J., 2014. "Verifying payoff security in the mixed extension of discontinuous games," Journal of Economic Theory, Elsevier, vol. 152(C), pages 291-303.
    21. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    22. Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August.
    23. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    24. Guilherme Carmona, 2016. "Reducible equilibrium properties: comments on recent existence results," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 431-455, March.
    25. 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.
    26. Pavlo Prokopovych, 2013. "The single deviation property in games with discontinuous payoffs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(2), pages 383-402, June.
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    Cited by:

    1. Amir, Rabah & Evstigneev, Igor V., 2018. "A new look at the classical Bertrand duopoly," Games and Economic Behavior, Elsevier, vol. 109(C), pages 99-103.
    2. János Flesch & P. Jean-Jacques Herings & Jasmine Maes & Arkadi Predtetchinski, 2022. "Individual upper semicontinuity and subgame perfect $$\epsilon $$ ϵ -equilibria in games with almost perfect information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 695-719, April.
    3. Flesch, Janos & Herings, P. Jean-Jacques & Maes, Jasmine & Predtetchinski, Arkadi, 2019. "Individual upper semicontinuity and subgame perfect ϵ-equilibria in games with almost perfect information," Research Memorandum 002, Maastricht University, Graduate School of Business and Economics (GSBE).
    4. Rabah Amir & Igor Evstigneev & Adriana Gama, 2021. "Oligopoly with network effects: firm-specific versus single network," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 1203-1230, April.
    5. Rabah Amir, 2018. "Special issue: supermodularity and monotone methods in economics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 547-556, October.
    6. Nikolai S. Kukushkin & Pierre von Mouche, 2018. "Cournot tatonnement and Nash equilibrium in binary status games," Economics Bulletin, AccessEcon, vol. 38(2), pages 1038-1044.
    7. Charlene Cosandier & Filomena Garcia & Malgorzata Knauff, 2018. "Price competition with differentiated goods and incomplete product awareness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 681-705, October.
    8. Łukasz Balbus & Paweł Dziewulski & Kevin Reffett & Łukasz Woźny, 2019. "A qualitative theory of large games with strategic complementarities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(3), pages 497-523, April.
    9. M. Ali Khan & Metin Uyanik, 2021. "The Yannelis–Prabhakar theorem on upper semi-continuous selections in paracompact spaces: extensions and applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 799-840, April.
    10. Kukushkin, Nikolai S., 2022. "Ordinal status games on networks," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    11. Finn Christensen, 2019. "Comparative statics and heterogeneity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(3), pages 665-702, April.
    12. Kukushkin, Nikolai S., 2018. "Better response dynamics and Nash equilibrium in discontinuous games," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 68-78.
    13. Amir, Rabah & De Castro, Luciano, 2017. "Nash equilibrium in games with quasi-monotonic best-responses," Journal of Economic Theory, Elsevier, vol. 172(C), pages 220-246.
    14. He, Wei & Sun, Yeneng, 2019. "Pure-strategy equilibria in Bayesian games," Journal of Economic Theory, Elsevier, vol. 180(C), pages 11-49.
    15. 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.
    16. Prokopovych, Pavlo & Yannelis, Nicholas C., 2019. "On monotone approximate and exact equilibria of an asymmetric first-price auction with affiliated private information," Journal of Economic Theory, Elsevier, vol. 184(C).
    17. Lu Yu, 2024. "Nash equilibria of quasisupermodular games," Papers 2406.13783, arXiv.org.

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    More about this item

    Keywords

    Discontinuous game; Strategic complementarities; Better-reply security; Directional single crossing; Increasing correspondence;
    All these keywords.

    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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