Weakly balanced contributions and solutions for cooperative games

Abstract We explore a relaxation of the balanced contributions property for solutions for TU games that requires the direction (sign) of one player’s change of payoffs when another player leaves the game to equal the direction (sign) of the latter player’s change of payoffs when the former leaves the game. There exists a large class of solutions that satisfy both efficiency and this weak balanced contributions property. The Shapley value is the unique solution that also obeys weak differential marginality.

[1]  Alvin E. Roth,et al.  The Shapley Value as a von Neumann-Morgenstern Utility , 1977 .

[2]  André Casajus,et al.  Weak differential marginality and the Shapley value , 2017, J. Econ. Theory.

[3]  Jagdish S. Gangolly.  On Joint Cost Allocation - Independent Cost Proportional Scheme (Icps) And Its Properties , 1981 .

[4]  E. Kalai,et al.  On weighted Shapley values , 1983 .

[5]  David Wettstein,et al.  Bidding for the Surplus : A Non-cooperative Approach to the Shapley Value , 2001, J. Econ. Theory.

[6]  Emilio Calvo,et al.  Potentials in cooperative TU-games , 1997 .

[7]  Emilio Calvo,et al.  Weighted weak semivalues , 2000, Int. J. Game Theory.

[8]  André Casajus,et al.  Differential marginality, van den Brink fairness, and the Shapley value , 2011 .

[9]  R. Myerson.  Conference structures and fair allocation rules , 1978 .

[10]  S. Tijs,et al.  Extensions of solution concepts by means of multiplicative å-games , 1986 .

[11]  Koji Yokote,et al.  The balanced contributions property for symmetric players , 2017, Oper. Res. Lett..

[12]  Éric Rémila,et al.  T he proportional Shapley value and an application , 2016 .

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

[14]  René van den Brink,et al.  An axiomatization of the Shapley value using a fairness property , 2002, Int. J. Game Theory.

[15]  S. Hart,et al.  Potential, value, and consistency , 1989 .

[16]  Sylvain Béal,et al.  Axiomatic characterizations under players nullification , 2016, Math. Soc. Sci..

[17]  Mamoru Kaneko,et al.  Utility Theories in Cooperative Games , 2004 .

[18]  K. Michael Ortmann.  Conservation of energy in value theory , 1998, Math. Methods Oper. Res..

[19]  Robert J. Weber,et al.  Probabilistic Values for Games , 1977 .

[20]  Yuan Ju,et al.  Implementing cooperative solution concepts: a generalized bidding approach , 2006 .

[21]  L. S. Shapley,et al.  17. A Value for n-Person Games , 1953 .