Theory and Decision

, Volume 69, Issue 2, pp 233–256 | Cite as

Characterization of dominance relations in finite coalitional games

Article

Abstract

McGarvey (Econometrica, 21(4), 608–610, 1953) has shown that any irreflexive and anti-symmetric relation can be obtained as a relation induced by majority rule. We address the analogous issue for dominance relations of finite cooperative games with non-transferable utility (coalitional NTU games). We find any irreflexive relation over a finite set can be obtained as the dominance relation of some finite coalitional NTU game. We also show that any such dominance relation is induced by a non-cooperative game through β-effectivity. Dominance relations obtainable through α-effectivity, however, have to comply with a more restrictive condition, which we refer to as the edge-mapping property.

Keywords

Cooperative game theory Non-transferable utility Dominance 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abdou J., Keiding H. (1991) Effectivity functions in social choice. Kluwer Academic Publishers, BostonGoogle Scholar
  2. Aumann R.J. (1959) Acceptable points in general n-person games. In: Tucker A.W., Luce R.D. (eds) Contributions to the theory of games IV, volume 40 of annals of mathematics studies. Princeton University Press, Princeton, pp 287–324Google Scholar
  3. Aumann R. J. (1961) The core of a cooperative game without side payments. Transactions of the American Mathematical Society 98: 539–552Google Scholar
  4. Aumann R. J., Peleg B. (1960) Von Neumann-Morgenstern solutions to cooperative games without side payments. Bulletin of the American Society 66: 173–179CrossRefGoogle Scholar
  5. Bergin J., Duggan J. (1999) An implementation-theoretic approach to non-cooperative foundations. Journal of Economic Theory 86: 50–76CrossRefGoogle Scholar
  6. Dutta B., Laslier J.-F. (1999) Comparison functions and choice correspondences. Social Choice and Welfare 16(4): 513–532CrossRefGoogle Scholar
  7. Farquharson R. (1969) Theory of voting. Yale University Press, New HeavenGoogle Scholar
  8. Fishburn P. C. (1977) Condorcet social choice functions. SIAM Journal on Applied Mathematics 33(3): 469–489CrossRefGoogle Scholar
  9. Hart S., MasColell M. (1996) Bargaining and value. Econometrica 64(2): 357–380CrossRefGoogle Scholar
  10. Kalai E., Samet D. (1985) Monotonic solution concepts to general cooperative games. Econometrica 53(2): 307–328CrossRefGoogle Scholar
  11. Kıbrıs Ö, Sertel M. R. (2007) Bargaining over a finite set of alternatives. Social Choice and Welfare 28: 421–437CrossRefGoogle Scholar
  12. Lahiri S. (2007) A weak bargaining set for contract choice problems. Research in Economics 61(4): 185–190CrossRefGoogle Scholar
  13. Laslier J.-F. (1997) Tournament solutions and majority voting. Springer-Verlag, HeidelbergGoogle Scholar
  14. Luce R.D., Raiffa H. (1957) Games and decisions: Introduction and critical survey. John Wiley & Sons, New YorkGoogle Scholar
  15. McGarvey D. C. (1953) A theorem on the construction of voting paradoxes. Econometrica 21(4): 608–610CrossRefGoogle Scholar
  16. Nash J. (1950) The bargaining problem. Econometrica 18: 155–162CrossRefGoogle Scholar
  17. Nash J. (1953) Two-person cooperative games. Econometrica 21: 128–140CrossRefGoogle Scholar
  18. Rubinstein A. (1982) Perfect equilibrium in a bargaining model. Econometrica 50(1): 97–109CrossRefGoogle Scholar
  19. Schwartz T. (1990) Cyclic tournaments and cooperative majority voting: A solution. Social Choice and Welfare 7: 19–29CrossRefGoogle Scholar
  20. Serrano R. (1997) A comment on the Nash program and the theory of implementation. Economic Letters 55: 203–208CrossRefGoogle Scholar
  21. Taylor A.D., Zwicker W.S. (1999) Simple games. Princeton, Princeton University PressGoogle Scholar
  22. von Neumann J., Morgenstern O. (1947) Theory of games and economic behavior, 2nd ed. Princeton University Press, PrincetonGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC. 2009

Authors and Affiliations

  1. 1.Ludwig-Maximilians-Universität MünchenMünchenGermany

Personalised recommendations