Skip to main content
SpringerLink
Log in

Monotonicity and Solidarity Axioms in Economics and Game Theory

  • Chapter
Rational Choice and Social Welfare

Part of the book series: Studies in Choice and Welfare ((WELFARE))

An important aspect of the complex notion of fairness in collective choices is that agents should bear responsibility only for their own actions. As a corollary, they should be treated ‘similarly’ when a change occurs for which no one is responsible. A minimal condition of ‘similar’ treatment is certainly that nobody benefits from such a change if someone else suffers from it.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Arin, J., & Inarra, E. (2001). Egalitarian solutions in the core. International Journal of Game Theory, 30, 187–193

    Article  Google Scholar 

  • Aumann, R. (1985). On the non-transferable utility value: A comment on the Roth-Shafer examples. Econometrica, 53, 667–677

    Article  Google Scholar 

  • Balasko, Y. (1979). Budget-constrained Pareto efficient allocations. Journal of Economic Theory, 21, 359–379

    Article  Google Scholar 

  • Champsaur, P., & Laroque, G. (1981). Fair allocations in large economies. Journal of Economic Theory, 25, 269–282

    Article  Google Scholar 

  • Chichilnisky, G., & Thomson, W. (1987). The Walrasian mechanism from equal division is not monotonic with respect to variations in the number of agents. Journal of Public Economics, 32, 119–124

    Article  Google Scholar 

  • Dubins, L., & Spanier, E. (1961). How to cut a cake fairly. American Mathematical Monthly, 68, 17

    Article  Google Scholar 

  • Dutta, B. (1990). The egalitarian solution and reduced game properties in convex games. International Journal of Game Theory, 19, 153–169

    Article  Google Scholar 

  • Dutta, B., & Ray, D. (1989). A concept of egalitarianism under participation constraints. Econometrica, 57, 465–479

    Article  Google Scholar 

  • Fleurbaey, M. (1996). Reward patterns of fair solutions. Journal of Public Economics, 59, 365–395

    Article  Google Scholar 

  • Foley, D. (1967). Resource allocation and the public sector. Yale Economic Essays, 7, 45–98

    Google Scholar 

  • Gaspart, F. (1996). A contribution to the theory of distributive justice (Ph. D. Thesis). FUNDP, Namur

    Google Scholar 

  • Geanakoplos, J., & Nalebuff, B. (1988). On a fundamental conflict between equity and efficiency (mimeo)

    Google Scholar 

  • Hokari, T. (2000). Population monotonic solutions on convex games. International Journal of Game Theory, 29, 327–338

    Article  Google Scholar 

  • Hokari, T. (2002). Monotone-path Dutta-Ray solutions on convex games. Social Choice and Welfare, 19, 825–844

    Article  Google Scholar 

  • Hougaard, J., & Osterdal, L. (2005). Monotonicity of social welfare optima (mimeo) University of Copenhagen.

    Google Scholar 

  • Hougaard, J., Peleg, B., & Osterdal, L. (2003). The Dutta-Ray solution on the class of convex games: A generalization and monotonicity properties (mimeo, forthcoming in International Journal of Game Theory)

    Google Scholar 

  • Hougaard, J., Peleg, B., & Thorlund-Petersen, L. (2001). On the set of Lorenz maximal imputations in the core of a balanced game. International Journal of Game Theory, 30, 147–165

    Article  Google Scholar 

  • Ichiishi, T. (1988). The cooperative nature of the firm (mimeo). Ohio State University

    Google Scholar 

  • Ichiishi, T. (1990). Comparative cooperative game theory. International Journal of Game Theory, 19, 139–152

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Kalai, E., & Smorodinsky, M. (1975). Other solutions to Nash’s bargaining problem. Econometrica, 43, 513–518

    Article  Google Scholar 

  • Keiding, H., & Moulin, H. (1991). The solidarity axiom in parametric surplus-sharing problems. Journal of Mathematical Economics, 20, 249–270

    Article  Google Scholar 

  • Kim, H. (2004). Population monotonic rules for fair allocation problems. Social Choice and Welfare, 23, 59–70

    Article  Google Scholar 

  • Koster, M. (2002). Hierarchical constrained egalitarianism in TU-games. Mathematical Social Sciences, 43, 251–265

    Article  Google Scholar 

  • Maniquet, F., & Sprumont, Y. (2000). On resource monotonicity in the fair division problem. Economics Letters, 68, 299–302

    Article  Google Scholar 

  • Marin-Solano, J., & Rafels, C. (1996). Convexity versus average convexity: Potential, PMAS, the Shapley value and simple games (mimeo). Universitat de Barcelona

    Google Scholar 

  • Meggido, N. (1974). On the non monotonicity of the bargaining set, the kernel, and the nucleolus of a game. SIAM Journal of Applied Mathematics, 27, 355–358

    Article  Google Scholar 

  • Moulin, H. (1990a). Cores and large cores when population varies. International Journal of Game Theory, 19, 219–232

    Article  Google Scholar 

  • Moulin, H. (1990b). Fair division under joint ownership: Recent results and open problems. Social Choice and Welfare, 7, 439–452

    Article  Google Scholar 

  • Moulin, H. (1991). Welfare bounds in the fair division problem. Journal of Economic Theory, 54, 321–337

    Article  Google Scholar 

  • Moulin, H. (1995). Cooperative microeconomics. Princeton: Princeton University Press

    Google Scholar 

  • Moulin, H., & Thomson, W. (1988). Can everyone benefit from growth? Two difficulties. Journal of Mathematical Economics, 17, 339–345

    Article  Google Scholar 

  • Neuefeind, W. (1972). On continuous utility. Journal of Economic Theory, 5, 174–176

    Article  Google Scholar 

  • Norde, H., & Reijnierse, H. (2002). A dual description of the class of games with a population monotonie allocation scheme. Games and Economic Behavior, 41, 322–343

    Article  Google Scholar 

  • Pazner, E., & Schmeidler, D. (1978). Egalitarian equivalent allocations: A new concept of economic equity. Quarterly Journal of Economics, 92, 671–687

    Article  Google Scholar 

  • Polterovich, V., & Spivak, V. (1983). Gross substitutability of point-to-set correspondences. Journal of Mathematical Economics, 92, 117–140

    Article  Google Scholar 

  • Rosenthal, E. (1990). Monotonicity of the core and value in dynamic cooperative games. International Journal of Game Theory, 19, 45–57

    Article  Google Scholar 

  • Shapley, L. (1953). A value for n-person games. In H. Khun & A. Tucker (Eds.), Contributions to the theory of games ii, annals of mathematics studies 28. Princeton, NJ: Princeton University Press

    Google Scholar 

  • Shapley, L. (1971). Cores of convex games. International Journal of Game Theory, 1, 1–26

    Article  Google Scholar 

  • Shubik, M. (1962). Incentives, decentralized control, the assignment of joint costs, and internal pricing. Management Science, 8, 325–343

    Article  Google Scholar 

  • Sprumont, Y. (1990). Population monotonic allocation schemes for cooperative games with transferable utility. Games and Economic Behavior, 2, 378–394

    Article  Google Scholar 

  • Sprumont, Y.(1996). Axiomatizing ordinal welfare egalitarianism when preferences may vary. Journal of Economic Theory, 68, 77–110

    Article  Google Scholar 

  • Sprumont, Y., & Zhou, L. (1999). Pazner-Schmeidler rules in large societies. Journal of Mathematical Economics, 31, 321–339

    Article  Google Scholar 

  • Steinhaus, H. (1948). The problem of fair division. Econometrica, 16, 101–104

    Google Scholar 

  • Thomson, W. (1983a). The fair division of a fixed supply among a growing population. Mathematics of Operations Research, 8, 319–326

    Article  Google Scholar 

  • Thomson, W. (1983b). Problems of fair division and the egalitarian solution. Journal of Economic Theory, 31, 211–226

    Article  Google Scholar 

  • Thomson, W. (1994). Notions of equal, or equivalent, opportunities. Social Choice and Welfare, 11, 137–156

    Google Scholar 

  • Thomson, W. (1995). Population-monotonic allocation rules. In W. Barnett, H. Moulin, M. Salles, & N. Schofield (Eds.), Social choice, welfare and ethics (pp. 79–124). Cambridge: Cambridge University Press

    Google Scholar 

  • Thomson, W. (1999). Règles dállocation monotones en ressources: une revue de la littérature. Revue Économique, 50, 757–796

    Google Scholar 

  • Thomson, W., & Myerson, R. (1980). Monotonicity and independence axioms. International Journal of Game Theory, 9, 37–49

    Article  Google Scholar 

  • Varian, H. (1976). Two problems in the theory of fairness. Journal of Public Economics, 5, 249–260

    Article  Google Scholar 

  • Young, P. (1980). Monotonie solutions of cooperative games. International Journal of Game Theory, 9, 37–49

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Département de Sciences Économiques and CIREQ, Université de Montréal, Canada

    Yves Sprumont

Authors
  1. Yves Sprumont
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Economics, University of California, Riverside, CA, 92521, USA

    Prasanta K. Pattanaik

  2. Department of Economics, Hitotsubashi University, 2-1 Naka, Kunitachi, Tokyo, 186-8601, Japan

    Koichi Tadenuma

  3. Department of Economics Andrew Young School of Policy Studies, Georgia State University, P.O. Box 3992, Atlanta, GA, 30302-3992, USA

    Yongsheng Xu

  4. Institute of Economic Research, Hitotsubashi University, 2-1 Naka, Kunitachi, Tokyo, 186-8603, Japan

    Naoki Yoshihara

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Sprumont, Y. (2008). Monotonicity and Solidarity Axioms in Economics and Game Theory. In: Pattanaik, P.K., Tadenuma, K., Xu, Y., Yoshihara, N. (eds) Rational Choice and Social Welfare. Studies in Choice and Welfare. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79832-3_5

Download citation

Publish with us

Policies and ethics

Search

Navigation