Monotonicity of social welfare optima

This paper considers the problem of maximizing social welfare subject to participation constraints. It is shown that for an income allocation method that maximizes a social welfare function there is a monotonic relationship between the incomes allocated to individual agents in a given coalition (with at least three members) and its participation constraint if and only if the aggregate income to that coalition is always maximized. An impossibility result demonstrates that there is no welfare maximizing allocation method in which agents' individual incomes monotonically increase in society's income. Thus, for any such allocation method, there are situations where some agents have incentives to prevent society in becoming richer.

[1]  H. Young.  Monotonic solutions of cooperative games , 1985 .

[2]  Satoru Fujishige,et al.  Lexicographically Optimal Base of a Polymatroid with Respect to a Weight Vector , 1980, Math. Oper. Res..

[3]  Dries Vermeulen,et al.  An axiomatic approach to egalitarianism in TU-games , 2008, Int. J. Game Theory.

[4]  R. Myerson,et al.  Monotonicity and independence axioms , 1980 .

[5]  E. Kalai,et al.  OTHER SOLUTIONS TO NASH'S BARGAINING PROBLEM , 1975 .

[6]  Debraj Ray,et al.  Constrained egalitarian allocations , 1991 .

[7]  E. Kalai.  Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons , 1977 .

[8]  E. Kohlberg.  On the Nucleolus of a Characteristic Function Game , 1971 .

[9]  Dries Vermeulen,et al.  Some characterizations of egalitarian solutions on classes of TU-games , 2003, Math. Soc. Sci..

[10]  Philip Wolfe,et al.  Contributions to the theory of games , 1953 .

[11]  Nimrod Megiddo,et al.  On the Nonmonotonicity of the Bargaining Set, the Kernel and the Nucleolus of Game , 1974 .

[12]  R. Jackson.  Inequalities , 2007, Algebra for Parents.

[13]  Maurice Koster.  Hierarchical constrained egalitarianism in TU-games , 2002, Math. Soc. Sci..

[14]  B. Peleg,et al.  Introduction to the Theory of Cooperative Games , 1983 .

[15]  Toru Hokari,et al.  The nucleolus is not aggregate-monotonic on the domain of convex games , 2000, Int. J. Game Theory.

[16]  Edward C. Rosenthal.  Monotonicity of the core and value in dynamic cooperative games , 1990 .

[17]  L. S. Shapley,et al.  Geometric Properties of the Kernel, Nucleolus, and Related Solution Concepts , 1979, Math. Oper. Res..

[18]  Jens Leth Hougaard,et al.  The Dutta-Ray Solution on the Class of Convex Games: a Generalization and Monotonicity Properties , 2005, IGTR.

[19]  Jens Leth Hougaard,et al.  On the set of Lorenz-maximal imputations in the core of a balanced game , 2001, Int. J. Game Theory.

[20]  P. Mongin,et al.  Constrained egalitarianism in a simple redistributive model , 2003 .

[21]  L. Shapley.  A Value for n-person Games , 1988 .

[22]  Dries Vermeulen,et al.  Geometry and Computation of the Lorenz Set , 2004, IGTR.

[23]  Javier Arin,et al.  Egalitarian solutions in the core , 2001, Int. J. Game Theory.

[24]  Toru Hokari,et al.  Monotone-path Dutta-Ray solutions on convex games , 2002, Soc. Choice Welf..

[25]  R. Toupin,et al.  Some properties of the Hessian Matrix of a Strictly Convex Function. , 1962 .

[26]  Flip Klijn,et al.  The egalitarian solution for convex games: some characterizations , 2000, Math. Soc. Sci..

[27]  E. Kalai,et al.  Monotonic Solutions to General Cooperative Games , 1985 .

[28]  L. Shapley.  Cores of convex games , 1971 .

[29]  Yves Sprumont.  Population monotonic allocation schemes for cooperative games with transferable utility , 1990 .

[30]  丸山 徹.  Convex Analysisの二,三の進展について , 1977 .

[31]  Debraj Ray,et al.  A Concept of Egalitarianism under Participation Constraints , 1989 .

[32]  Bhaskar Dutta.  The egalitarian solution and reduced game properties in convex games , 1990 .