Population solidarity, population fair-ranking, and the egalitarian value

We investigate the implications of two axioms specifying how a value should respond to changes in the set of players for TU games. Population solidarity requires that the arrival of new players should affect all the original players in the same direction: all gain together or all lose together. On the other hand, population fair-ranking requires that the arrival of new players should not affect the relative positions of the original players. As a result, we obtain characterizations of the egalitarian value, which assigns to each player an equal share over an individual utility level. It is the only value satisfying either one of the two axioms together with efficiency, symmetry and strategic equivalence.

[1]  R. Aumann,et al.  Game theoretic analysis of a bankruptcy problem from the Talmud , 1985 .

[2]  William Thomson,et al.  Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey , 2003, Math. Soc. Sci..

[3]  William Thomson,et al.  Cost allocation and airport problems , 2007 .

[4]  W. Thomson.  Problems of fair division and the Egalitarian solution , 1983 .

[5]  T. Driessen,et al.  Coincidence of and collinearity between game theoretic solutions , 1991 .

[6]  Barry O'Neill,et al.  A problem of rights arbitration from the Talmud , 1982, Math. Soc. Sci..

[7]  Y. Chun.  The solidarity axiom for quasi-linear social choice problems , 1986 .

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

[9]  Roger B. Myerson,et al.  Graphs and Cooperation in Games , 1977, Math. Oper. Res..

[10]  William A. Barnett,et al.  Social Choice, Welfare, and Ethics , 2006 .

[11]  Youngsub Chun,et al.  A new axiomatization of the shapley value , 1989 .

[12]  G. Owen,et al.  A Simple Expression for the Shapley Value in a Special Case , 1973 .

[13]  Yukihiko Funaki,et al.  Reduced Game Properties of Egalitarian Division Rules for TU-Games , 1997 .

[14]  Debraj Ray,et al.  Game-Theoretical Applications to Economics and Operations Research , 1997 .

[15]  René van den Brink,et al.  Null or nullifying players: The difference between the Shapley value and equal division solutions , 2007, J. Econ. Theory.

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

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

[18]  Yukihiko Funaki,et al.  Axiomatizations of a Class of Equal Surplus Sharing Solutions for TU-Games , 2009 .