Skip to main content
SpringerLink
Log in

Consistency and monotonicity in assignment problems

  • Published:
International Journal of Game Theory Aims and scope Submit manuscript

Abstract

This paper presents axiomatic characterizations of the core of assignment problems. In the main axiomatization theorem we use six axioms including the consistency (CONS) and the weak pairwise-monotonicity (W.P.MON) which are firstly proposed and defined for this setup in the present paper. Since an assignment problem may be converted into a model of a private ownership economy with indivisible goods and the core of the assignment problem coincides with the set of the competitive allocations of the economy, our characterization theorems also give axiomatic characterizations of the set of competitive allocations. Because the consistency is a desirable property of resource allocation mechanisms, our main result gives a new normative implication of competitive equilibria.

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

  • Demange G, Gale D (1985) The strategy structure of two-sided matching markets. Econometrica 53: 873–888

    Google Scholar 

  • Demange G, Gale D, Sotomayor M (1986) Multi-item auctions. Journal of Political Economy 94: 863–872

    Google Scholar 

  • Gale D, Shapley L (1962) College admissions and the stability of marriage. American Mathematical Monthly 69: 9–15

    Google Scholar 

  • Hildenbrand W (1974) Core and equilibria of a large economy. Princeton Univ Press, Princeton New Jersey

    Google Scholar 

  • Kalai E (1977) Proportional solutions to bargaining situations: Interpersonal utility comparisons. Econometrica 45: 1623–1630

    Google Scholar 

  • Moulin H (1988) Axioms of cooperative decision making. Cambridge Univ Press, Cambridge UK

    Google Scholar 

  • Moulin H (1992) An application of the shapley value to fair division with money. Econometrica 60: 1331–1349

    Google Scholar 

  • Peleg B (1985) An axiomatization of the core of cooperative games without side-payments. Journal of Mathematical Economics 14: 203–214

    Google Scholar 

  • Peleg B (1986) On the reduced game property and its converse. International Journal of Game Theory 15: 187–200

    Google Scholar 

  • Peleg B (1989) An axiomatization of the core of market games. Mathematics of Operations Research 14: 448–456

    Google Scholar 

  • Peleg B (1992) Axiomatizations of the core. In: Aumann RJ, Hart S (eds) Handbook of Game Theory with Economic Applications, North-Holland Amsterdam Netherlands

    Google Scholar 

  • Roth A, Sotomayor M (1990) Two-sided matching: A study in game-theoretic modelling and analysis. Cambridge Univ Press Cambridge UK

    Google Scholar 

  • Roth A, Sotomayor M (1992) Two-sided matching. In: Aumann RJ, Hart S (eds) Handbook of Game Theory with Economic Applications, North-Holland Amsterdam Netherlands

    Google Scholar 

  • Sasaki H, Toda M (1992) Consistency and characterization of the core of two-sided matching problems. Journal of Economic Theory 56: 218–227

    Google Scholar 

  • Shapley L, Shubik M (1969) On market games. Journal of Economic Theory 1: 9–25

    Google Scholar 

  • Shapley L, Shubik M (1972) The assignment game I: The core. International Journal of Game Theory 1: 111–130

    Google Scholar 

  • Tadenuma K (1992) Reduced games, consistency, and the core. International Journal of Game Theory 20: 325–334

    Google Scholar 

  • Tadenuma K, Thomson W (1991) No-envy and consistency in economies with indivisible goods. Econometrica 59: 1755–1767

    Google Scholar 

  • Thomson W (1988) A study of choice correspondences in economies with a variable number of agents. Journal of Economic Theory 46: 237–254

    Google Scholar 

  • Thomson W (1990) The consistency principle. In: Ichiishi T, Neyman A, Tauman Y (eds) Game Theory and Applications, Academic Press 187–215

  • Thomson W (1992a) Consistent extensions. Rochester Center for Economic Research Working Paper 329

  • Thomson W (1992b) Consistency in exchange economies. University of Rochester, Mimeo

    Google Scholar 

  • Thomson W (1992c) Consistent allocation rules. University of Rochester, Mimeo

    Google Scholar 

  • Thomson W.L, Zhou L (1993) Consistent solutions in atomless economies. Econometrica 61: 575–587

    Google Scholar 

  • Young HP (1985) Monotonic solutions of cooperative games. International Journal of Game Theory 14: 65–72

    Google Scholar 

  • Zhou L (1991) A weak monotonicity property of the nucleolus. Internatonal Journal of Game Theory 19: 407–411

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Commerce, Waseda University, Nishi-Waseda, Shinjuku-ku, 169-50, Tokyo, Japan

    Hiroo Sasaki

Authors
  1. Hiroo Sasaki
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sasaki, H. Consistency and monotonicity in assignment problems. Int J Game Theory 24, 373–397 (1995). https://doi.org/10.1007/BF01243039

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01243039

Keywords

Search

Navigation