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Games with Strategic Complements and Substitutes

Author

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  • Andrew Monaco

    (Department of Economics, University of Puget Sound)

  • Tarun Sabarwal

    (Department of Economics, University of Kansas)

Abstract

This paper studies games with both strategic substitutes and strategic complements, and more generally, games with strategic heterogeneity (GSH). Such games may behave differently from either games with strategic complements or games with strategic sub- stitutes. Under mild assumptions (on one or two players only), the equilibrium set in a GSH is totally unordered (no two equilibria are comparable in the standard product order). Moreover, under mild assumptions (on one player only), parameterized GSH do not allow decreasing equilibrium selections. In general, this cannot be strengthened to conclude increasing selections. Monotone comparative statics results are presented for games in which some players exhibit strategic substitutes and others exhibit strategic complements. For two-player games with linearly ordered strategy spaces, there is a char- acterization. More generally, there are sufficient conditions. The conditions apply only to players exhibiting strategic substitutes; no additional conditions are needed for players with strategic complements. Several examples highlight the results.

Suggested Citation

  • Andrew Monaco & Tarun Sabarwal, 2015. "Games with Strategic Complements and Substitutes," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201408, University of Kansas, Department of Economics, revised Jan 2015.
  • Handle: RePEc:kan:wpaper:2011408
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    File URL: http://www2.ku.edu/~kuwpaper/2014Papers/201408.pdf
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Tarun Sabarwal & Hoa VuXuan, 2018. "Two Stage 2 × 2 Games With Strategic Substitutes and Strategic Heterogeneity," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201902, University of Kansas, Department of Economics.
    2. 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.
    3. Cao, Zhigang & Chen, Xujin & Qin, Cheng-Zhong & Wang, Changjun & Yang, Xiaoguang, 2018. "Embedding games with strategic complements into games with strategic substitutes," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 45-51.
    4. M. Castellani & L. Fanelli & M. Savioli, 2015. "Government fiscal efforts vs. labour union strikes. Strategic substitutes or complements?," Working Papers wp1013, Dipartimento Scienze Economiche, Universita' di Bologna.
    5. Alexei Alexandrov & Özlem Bedre-Defolie, 2015. "LeChatelier-Samuelson principle in games and pass-through of shocks," ESMT Research Working Papers ESMT-15-03, ESMT European School of Management and Technology, revised 01 Mar 2016.
    6. Anne-Christine Barthel & Tarun Sabarwal, 2018. "Directional monotone comparative statics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 557-591, October.
    7. 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.
    8. Eric J. Hoffmann & Tarun Sabarwal, 2019. "Equilibrium existence in global games with general payoff structures," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(1), pages 105-115, May.
    9. Magnus Hoffmann & Grégoire Rota‐Graziosi, 2020. "Endogenous timing in the presence of non‐monotonicities," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 53(1), pages 359-402, February.
    10. Berman, Ron & Heller, Yuval, 2020. "Naive Analytics Equilibrium," MPRA Paper 103824, University Library of Munich, Germany.
    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. Christian Ewerhart, 2020. "Ordinal potentials in smooth games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 1069-1100, November.
    13. repec:kan:wpaper:201502 is not listed on IDEAS
    14. Anne-Christine Barthel & Eric Hoffmann & Tarun Sabarwal, 2021. "A Unified Approach to p-Dominance and its Generalizations in Games with Strategic Complements and Substitutes," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202109, University of Kansas, Department of Economics.
    15. Martin Kaae Jensen, 2015. "Existence, Uniqueness, and Comparative Statics in Contests," Discussion Papers in Economics 15/16, Division of Economics, School of Business, University of Leicester.
    16. Lauren Russell, 2021. "Price Effects of Nonprofit College and University Mergers," The Review of Economics and Statistics, MIT Press, vol. 103(1), pages 88-101, March.
    17. Rabah Amir, 2019. "Supermodularity and Complementarity in Economic Theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(3), pages 487-496, April.
    18. 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.
    19. 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.
    20. Alexandrov, Alexei & Bedre-Defolie, Özlem, 2017. "LeChatelier–Samuelson principle in games and pass-through of shocks," Journal of Economic Theory, Elsevier, vol. 168(C), pages 44-54.
    21. Eric Hoffmann & Tarun Sabarwal, 2015. "A Global Game with Strategic Substitutes and Complements: Note," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201409, University of Kansas, Department of Economics.
    22. repec:kan:wpaper:201412 is not listed on IDEAS
    23. Christian Ewerhart & Julia Lareida, 2018. "Voluntary disclosure in asymmetric contests," ECON - Working Papers 279, Department of Economics - University of Zurich, revised Jan 2021.
    24. Anne-Christine Barthel & Eric Hoffmann, 2020. "Characterizing monotone games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 1045-1068, November.

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    More about this item

    Keywords

    Lattice games; strategic complements; strategic substitutes; strategic hetero- geneity; equilibrium set; monotone comparative statics;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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