Skip to main content
SpringerLink
Log in

Aggregative games and best-reply potentials

  • Research Article
  • Published:
Economic Theory Aims and scope Submit manuscript

Abstract

This paper introduces quasi-aggregative games and establishes conditions under which such games admit a best-reply potential. This implies existence of a pure strategy Nash equilibrium without any convexity or quasi-concavity assumptions. It also implies convergence of best-reply dynamics under some additional assumptions. Most of the existing literature’s aggregation concepts are special cases of quasi-aggregative games, and many new situations are allowed for. An example is payoff functions that depend on own strategies as well as a linear combination of the mean and the variance of players’ strategies.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Aczél, J.: Lectures on Functional Equations and Their Applications. Dover Publications, Mineola. (Unabridged version of the original 1966 Academic Press Edition) (2006)

  • Agerwal R.P.: Difference Equations and Inequalities: Theory, Methods, and Applications, 2nd edn. Marcel-Dekker, New York (2000)

    Google Scholar 

  • Alos-Ferrer C., Ania A.B.: The evolutionary stability of perfectly competitive behaviour. Econ Theory 26, 497–516 (2005)

    Article  Google Scholar 

  • Amir R.: Sensitivity analysis of multisector optimal economic dynamics. J Math Econ 25, 123–141 (1996)

    Article  Google Scholar 

  • Cornes, R., Hartley, R.: Disguised Aggregative Games, Discussion Paper 1/11. University of Nottingham (2001)

  • Cournot, A.: Recherches sur les Principes Mathematiques de la Theorie des Richesses, Paris: Hachette. (English translation by N. T. Bacon, Macmillan, 1897) (1838)

  • Dubey P., Haimanko O., Zapechelnyuk A.: Strategic complements and substitutes, and potential games. Games Econ Behav 54, 77–94 (2006)

    Article  Google Scholar 

  • Edlin A., Shannon C.: Strict monotonicity in comparative statics. J Econ Theory 81, 201–219 (1998)

    Article  Google Scholar 

  • Gordon R.A.: The integrals of Lebesgue, Denjoy, Perron, and Henstock. Am Math Soc, Providence (1994)

    Google Scholar 

  • Gorman W.M.: The structure of utility functions. Rev Econ Stud 35, 367–390 (1968)

    Article  Google Scholar 

  • Huang, Z.: Fictitious play in games with a continuum of strategies, PhD Thesis, Department of Economics, State University of New York, Stony Brook (2002)

  • Jensen M.K.: Aggregative Games, Discussion Paper No. 06–10. University of Birmingham, Birmingham (2006)

    Google Scholar 

  • Jensen M.K.: Monotone comparative statics in ordered vector spaces. B E J Theor Econ 7, 1 (2007a) Article 35

    Google Scholar 

  • Jensen M.K.: Stability of pure strategy nash equilibrium in best-reply potential games. University of Birmingham, Mimeo (2007b)

    Google Scholar 

  • Kockesen L., Ok E., Sethi R.: Evolution of interdependent preferences in aggregative games. Games Econ Behav 31, 303–310 (2000)

    Article  Google Scholar 

  • Kukushkin N.S.: A fixed-point theorem for decreasing mappings. Econ Lett 46, 23–26 (1994)

    Article  Google Scholar 

  • Kukushkin N.S.: Best response dynamics in finite games with additive aggregation. Games Econ Behav 48, 94–110 (2004)

    Article  Google Scholar 

  • Kukushkin N.S.: Strategic supplements in games with polylinear interactions. Russian Academy of Sciences, Mimeo (2005)

    Google Scholar 

  • Morris S., Ui T.: Best response equivalence. Games Econ Behav 49, 260–287 (2004)

    Article  Google Scholar 

  • Novshek W.: On the existence of cournot equilibrium. Rev Econ Stud 52, 86–98 (1985)

    Google Scholar 

  • Possajennikov A.: Evolutionary foundation of aggregative-taking behavior. Econ Theory 21, 921–928 (2003)

    Article  Google Scholar 

  • Schipper B.: The evolutionary stability of optimism, pessimism and complete ignorance. University of California at Davis, Mimeo (2005)

    Google Scholar 

  • Topkis D.M.: Supermodularity and complementarity. Princeton University Press, New Jersey (1998)

    Google Scholar 

  • Vind, K., Grodal, B.: Independence, Additivity, Uncertainty. Berlin: Springer (2003) (Studies in Economic Theory, vol. 14)

  • Voorneveld M.: Best-response potential games. Econ Lett 66, 289–295 (2000)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Economics, University of Birmingham, 90 Vincent Drive, Birmingham, B15 2TT, UK

    Martin Kaae Jensen

Authors
  1. Martin Kaae Jensen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Martin Kaae Jensen.

Additional information

I would like to thank Daron Acemoglu, Burkhard Schipper, and an anonymous referee for their helpful remarks and comments. Thanks also to seminar participants at the University of Copenhagen and University of Warwick.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jensen, M.K. Aggregative games and best-reply potentials. Econ Theory 43, 45–66 (2010). https://doi.org/10.1007/s00199-008-0419-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00199-008-0419-8

Keywords

JEL Classification

Search

Navigation