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Games with strategic complements and substitutes

Author

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  • Andrew J. Monaco

    () (University of Puget Sound)

  • Tarun Sabarwal

    () (University of Kansas)

Abstract

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 substitutes. 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 characterization. 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 J. Monaco & Tarun Sabarwal, 2016. "Games with strategic complements and substitutes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(1), pages 65-91, June.
  • Handle: RePEc:spr:joecth:v:62:y:2016:i:1:d:10.1007_s00199-015-0864-0 DOI: 10.1007/s00199-015-0864-0
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Christian Ewerhart, 2017. "Ordinal potentials in smooth games," ECON - Working Papers 265, Department of Economics - University of Zurich.
    4. repec:kan:wpaper:201502 is not listed on IDEAS
    5. Martin Kaae Jensen, 2015. "Existence, Uniqueness, and Comparative Statics in Contests," Discussion Papers in Economics 15/16, Department of Economics, University of Leicester.
    6. repec:eee:jetheo:v:172:y:2017:i:c:p:220-246 is not listed on IDEAS
    7. 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.
    8. 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.
    9. repec:kan:wpaper:201412 is not listed on IDEAS
    10. Anne-Christine Barthel & Tarun Sabarwal, 2016. "Directional Monotone Comparative Statics," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201601, University of Kansas, Department of Economics.

    More about this item

    Keywords

    Lattice games; Strategic complements; Strategic substitutes; Strategic heterogeneity; Equilibrium set; Monotone comparative statics;

    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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