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International Journal of Game Theory

, Volume 45, Issue 3, pp 743–768 | Cite as

Modeling cooperative decision situations: the deviation function form and the equilibrium concept

  • Marilda SotomayorEmail author
Original Paper

Abstract

Rosenthal (J Econ Theory 5:88–101, 1972) points out that the coalitional function form may be insufficient to analyze some strategic interactions of the cooperative normal form. His solution consists in representing games in effectiveness form, which explicitly describes the set of possible outcomes that each coalition can enforce by a unilateral deviation from each proposed outcome. The present paper detects some non-appropriateness of the effectiveness representation with respect to the stability of outcomes against coalitional deviations. In order to correct such inadequacies, we propose a new model, called deviation function form. The novelty is that, besides providing a detailed description of an outcome, the model captures new kinds of coalitional interactions that support the agreements proposed by deviating coalitions and that cannot be identified via the effectiveness form. Furthermore, it can be used to model the existent matching markets. Its formulation allows defining a new solution concept, which characterizes the cooperative equilibria and extends the stability concept of the existent matching models. The connection between the core and the cooperative equilibrium concepts is established.

Keywords

Cooperative equilibrium Core Stability Matching 

JEL Classification

C78 D78 

References

  1. Aumann R (1967) A survey of cooperative games without side payments. In: Shubik M (ed) Essays in mathematical economics. Princeton University Press, Princeton, pp 3–22Google Scholar
  2. Blair C (1988) The lattice structure of the set of stable matchings with multiple partners. Math Oper Res 13:619–628CrossRefGoogle Scholar
  3. Gale D, Shapley L (1962) College admissions and the stability of marriage. Am Math Mon 69:9–15CrossRefGoogle Scholar
  4. Kelso A, Crawford V (1982) Job matching, coalition formation and gross substitutes. Econometrica 50:1483–1504CrossRefGoogle Scholar
  5. Rosenthal R (1972) Cooperative games in effectiveness form. J Econ Theory 5:88–101CrossRefGoogle Scholar
  6. Roth A (1984) Stability and polarization of interests in job matching. Econometrica 52:47–57CrossRefGoogle Scholar
  7. Roth A (1985) The college admission problem is not equivalent to the marriage problem. J Econ Theory 36:277–288CrossRefGoogle Scholar
  8. Roth A, Sotomayor M (1990) Two-sided matching. A study in game theoretic modeling and analysis. In: Econometric society monographs no. 18. Cambridge University Press, CambridgeGoogle Scholar
  9. Shapley L, Shubik M (1972) The assignment game I: the core. Int J Game Theory 1:111–130CrossRefGoogle Scholar
  10. Sotomayor (1992) The multiple partners game. In: Majumdar M (ed) Equilibrium and dynamics—essays in honor of David Gale. McMillian Press, New YorkGoogle Scholar
  11. Sotomayor M (1999) Three remarks on the many-to-many stable matching problem. Math Soc Sci 38:55–70Google Scholar
  12. Sotomayor M (2007) Connecting the cooperative and competitive structures of the multiple-partners assignment game. J Econ Theory 134:155–174Google Scholar
  13. Sotomayor M (2010) Stability property of matchings is a natural solution concept in coalitional market games. Int J Game Theory 39:237–248Google Scholar
  14. Sotomayor M (2011) The pareto-stability concept is a natural solution concept for discrete matching markets with indifferences. Int J Game Theory 40:631–644Google Scholar
  15. Sotomayor M (2012) Labor time shared in the assignment game lending new insights to the theory of two-sided matching markets. MimeoGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Graduate School of Economics of FGVRio de JaneiroBrazil
  2. 2.Department of EconomicsUniversity of São PauloSão PauloBrazil

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