International Journal of Game Theory

, Volume 44, Issue 4, pp 785–813 | Cite as

Coalition-proofness in a class of games with strategic substitutes

  • Federico Quartieri
  • Ryusuke Shinohara


We examine the coalition-proofness and Pareto properties of Nash equilibria in pure strategy \(\sigma \)-interactive games with strategic substitutes and increasing/decreasing externalities. For this class of games: (i) we prove the equivalence among the set of Nash equilibria, the set of coalition-proof Nash equilibria under strong Pareto dominance and the set of Nash equilibria that are not strongly Pareto dominated by other Nash equilibria; (ii) we prove that the fixpoints of some “ extremal” selections from the joint best reply correspondence are both coalition-proof Nash equilibria under weak Pareto dominance and not weakly Pareto dominated by other Nash equilibria. We also provide an order-theoretic characterization of the set of Nash equilibria and show various applications of our results.


Coalition-proof Nash equilibrium Pareto dominance  Strategic substitutes Externalities Generalized aggregative games 



The present version of this paper considerably benefited from discerning comments and remarks of two anonymous reviewers. The second author gratefully acknowledges financial support from Grant-in-Aid for Young Scientists (21730156, 24730165) from the Japan Society for Promotion of Science.


  1. Acemoglu D, Jensen MK (2013) Aggregate comparative statics. Games Econ Behav 81:27–49MATHMathSciNetCrossRefGoogle Scholar
  2. Alós-Ferrer C, Ania AB (2005) The evolutionary logic of perfectly competitive behaviour. Econ Theory 26:497–516MATHCrossRefGoogle Scholar
  3. Amir R (1996) Cournot oligopoly and the theory of supermodular games. Games Econ Behav 15:132–148MATHMathSciNetCrossRefGoogle Scholar
  4. Bernheim D, Peleg B, Whinston M (1987) Coalition-proof Nash equilibria I: concepts. J Econ Theory 42:1–12MATHMathSciNetCrossRefGoogle Scholar
  5. Bramoullé Y, Kranton R (2007) Public goods in networks. J Econ Theory 135:478–494MATHCrossRefGoogle Scholar
  6. Bulow JI, Geanakoplos JD, Klemperer PD (1985) Multimarket oligopoly: Strategic substitutes and complements. J Polit Econ 93:488–511CrossRefGoogle Scholar
  7. Corchón L (1994) Comparative statics for aggregative games. The strong concavity case. Math Soc Sci 28:151–165MATHCrossRefGoogle Scholar
  8. Dacić RM (1979) Fixed points of antitone mappings in conditionally complete partially ordered sets. Publ Inst Math 40:83–90Google Scholar
  9. Dubey P, Haimanko O, Zapechelnyuk A (2006) Strategic complements and substitutes, and potential games. Games Econ Behav 54:77–94MATHMathSciNetCrossRefGoogle Scholar
  10. Furusawa T, Konishi H (2011) Contributing or free-riding? voluntary participation in a public good economy. Theor econ 6:219–256Google Scholar
  11. Jackson MO, Zenou Y (2014) Games on networks. In: Young P, Zamir S (eds), Handbook of game theory, vol 4. Elsevier Publisher, AmsterdamGoogle Scholar
  12. Jensen MK (2006) Existence, comparative statics, and stability in games with strategic substitutes. Working paper, Department of Economics, University of BirminghamGoogle Scholar
  13. Jensen MK (2010) Aggregative games and best-reply potentials. Econ Theory 43:45–66MATHCrossRefGoogle Scholar
  14. Jensen MK (2012) Aggregative games and best-reply potentials: Erratum. Available at
  15. Kerschbamer R, Puppe C (1998) Voluntary contributions when the public good is not necessarily normal. J Econ 68:175–192MATHCrossRefGoogle Scholar
  16. Konishi H, Le Breton M, Weber S (1999) On coalition-proof Nash equilibria in common agency games. J Econ Theory 85:122–139Google Scholar
  17. Kukushkin NS (1994) A fixed-point theorem for decreasing mappings. Econ Lett 46:23–26Google Scholar
  18. Kukushkin NS (1997) An existence result for coalition-proof equilibrium. Econ Lett 57:269–273MATHMathSciNetCrossRefGoogle Scholar
  19. Kukushkin NS (2005) Strategic supplements in games with polylinear interactions, Available at
  20. Milgrom P, Roberts J (1990) Rationalizability, learning and equilibrium in games with strategic complementarities. Econometrica 58:1255–1277MATHMathSciNetCrossRefGoogle Scholar
  21. Milgrom P, Roberts J (1996) Coalition-proofness and correlation with arbitrary communication possibilities. Games Econ Behav 17:113–128MathSciNetCrossRefGoogle Scholar
  22. Novshek W (1985) On the existence of Cournot equilibrium. Rev Econ Stud 52:85–98MATHMathSciNetCrossRefGoogle Scholar
  23. Newton J (2010) Coalitional behaviour and the provision of public goods on networks. Cambridge University, Working paper.Google Scholar
  24. Quartieri F (2013) Coalition-proofness under weak and strong Pareto dominance. Soc Choice Welf 40:553–579MATHMathSciNetCrossRefGoogle Scholar
  25. Quartieri F, Shinohara R (2012) Coalition-proofness in aggregative games with strategic substitutes and externalities, Available at
  26. Roy S, Sabarwal T (2008) On the (non-)lattice structure of the equilibrium set in games with strategic substitutes. Econ Theory 37:161–169MATHMathSciNetCrossRefGoogle Scholar
  27. Shinohara R (2005) Coalition-proofness and dominance relations. Econ Lett 89:174–179MATHMathSciNetCrossRefGoogle Scholar
  28. Yi S (1999) On the coalition-proofness of the Pareto frontier of the set of Nash equilibria. Games Econ Behav 26:353–364MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Dipartimento di scienze economiche e statisticheUniversità degli studi di Napoli Federico IINaplesItaly
  2. 2.Faculty of EconomicsHosei UniversityMachidaJapan

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