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, Volume 15, Issue 1, pp 138–145 | Cite as

Multicriteria games and potentials

  • Fioravante Patrone
  • Lucia PusilloEmail author
  • Stef Tijs
Open Access
Original Paper

Abstract

In this note we study how far the theory of strategic games with potentials, as reported by Monderer and Shapley (Games Econ Behav 14:124–143, 1996), can be extended to strategic games with vector payoffs, as reported by Shapley (Nav Res Logist Q 6:57–61, 1959). The problem of the existence of pure approximate Pareto equilibria for multicriteria potential games is also studied.

Keywords

Noncooperative potential games Multicriteria Pareto equilibria Approximate Pareto equilibria Supermodularity 

Mathematics Subject Classification (2000)

91A10 

References

  1. Branzei R, Mallozzi L, Tijs S (2003) Supermodular games and potential games. J Math Econ 39:39–49 CrossRefGoogle Scholar
  2. Borm PEM, Tijs SH, van den Aarssen JCM (1989) Pareto equilibria in multiobjective games. Methods Oper Res 60:303–312 Google Scholar
  3. Facchini G, Van Megen F, Borm P, Tijs S (1997) Congestion models and weighted Bayesian potential games. Theory Decis 42:193–206 CrossRefGoogle Scholar
  4. Margiocco M, Pusillo L (2007) Stackelberg well-posedness and hierarchical potential games. In: Jorgensen S, Quincampoix M, Vincent TL (eds) Advances in dynamic game theory. Numerical methods, algorithms and applications to ecology and economics. Annals of the international society of dynamic games, vol 9 (to appear) Google Scholar
  5. Monderer D, Shapley LS (1996) Potential games. Games Econ Behav 14:124–143 CrossRefGoogle Scholar
  6. Norde H, Patrone F (2002) A potential approach for ordinal games. Top 9:69–75 CrossRefGoogle Scholar
  7. Norde H, Tijs S (1998) Determinateness of strategic games with potential. Math Methods Oper Res 48:377–385 CrossRefGoogle Scholar
  8. Peleg B, Potters J, Tijs S (1996) Minimality of consistent solutions for strategic games, in particular for potential games. Econ Theory 7:81–93 CrossRefGoogle Scholar
  9. Potters J, Raghavan TES, Tijs S (1999) Pure equilibrium strategies for stochastic games via potential functions. Report No. 9910, Department of Mathematics, University of Nijmegen, The Netherlands Google Scholar
  10. Rosenthal RW (1973) A class of games possessing pure strategy Nash equilibria. Int J Game Theory 2:65–67 CrossRefGoogle Scholar
  11. Shapley LS (1959) Equilibrium points in games with vector payoffs. Nav Res Logist Q 6:57–61 CrossRefGoogle Scholar
  12. Slade ME (1994) What does an oligopoly maximize?. J Ind Econ 42:45–61 CrossRefGoogle Scholar
  13. Topkis D (1998) Supermodularity and complementarity. Princeton University Press, Princeton Google Scholar
  14. Voorneveld M (1999) Potential games and interactive decisions with multiple criteria. Dissertation series No. 61, CentER of Economic Research, Tilburg University, The Netherlands Google Scholar
  15. Voorneveld M, Norde H (1997) A characterization of ordinal potential games. Games Econ Behav 19:235–242 CrossRefGoogle Scholar
  16. Voorneveld M, Tijs S, Mallozzi L (1998) Sequential production situations and potentials In: Garcia-Jurado I, Patrone F, Tijs S (eds) Game practice: contributions from applied game theory. Kluwer Academic, Dordrecht Google Scholar

Copyright information

© Sociedad de Estadística e Investigación Operativa 2007

Authors and Affiliations

  1. 1.DIPTEM, Sezione Metodi e Modelli Matematici, Facoltà di IngegneriaUniversity of GenoaGenoaItaly
  2. 2.DIMA, Department of MathematicsUniversity of GenoaGenoaItaly
  3. 3.CentER and Department of Econometrics and Operations ResearchTilburg UniversityTilburgThe Netherlands

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