An Introduction to Allocation Rules

Motivation and a Few Cases.- Simple Sharing Problems.- Cost Allocation as Cooperative Games.- General Sharing Problems.- Sharing in Networks.

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

[2]  John C. Harsanyi,et al.  Nonlinear social welfare functions , 1975 .

[3]  Steven J. Brams,et al.  Fair division - from cake-cutting to dispute resolution , 1998 .

[4]  Lloyd S. Shapley,et al.  On balanced sets and cores , 1967 .

[5]  Herbert Hamers,et al.  Cost allocation in a bank ATM network , 2004, Math. Methods Oper. Res..

[6]  Youngsub Chun,et al.  Equivalence of axioms for bankruptcy problems , 1999, Int. J. Game Theory.

[7]  J. S. Ransmeier,et al.  The Tennessee Valley Authority : a case study in the economics of multiple purpose stream planning , 1943 .

[8]  Hervé Moulin,et al.  Axiomatic cost and surplus sharing , 2002 .

[9]  M. Shubik.  Incentives, Decentralized Control, the Assignment of Joint Costs and Internal Pricing , 1962 .

[10]  David Aadland,et al.  Shared irrigation costs: An empirical and axiomatic analysis , 1998 .

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

[12]  M. Angeles de Frutos.  Decreasing Serial Cost Sharing under Economies of Scale , 1998 .

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

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

[15]  Stef Tijs.  An axiomatization of the τ-value , 1987 .

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

[17]  I. Olkin,et al.  Inequalities: Theory of Majorization and Its Applications , 1980 .

[18]  D. Schmeidler.  The Nucleolus of a Characteristic Function Game , 1969 .

[19]  N. Meyers,et al.  H = W. , 1964, Proceedings of the National Academy of Sciences of the United States of America.

[20]  Jeroen Suijs.  Cooperative Decision-Making Under Risk , 1999 .

[21]  Patrick Moyes.  Inequality Reducing and Inequality Preserving Transformations of Incomes: Symmetric and Individualistic Transformations , 1994 .

[22]  H. Young,et al.  Distributive justice in taxation , 1988 .

[23]  Vijay Govindarajan,et al.  Strategic Cost Management , 1993 .

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

[25]  Jens Leth Hougaard,et al.  Monotonicity of social welfare optima , 2010, Games Econ. Behav..

[26]  J. Rawls,et al.  Some Reasons for the Maximin Criterion , 1974 .

[27]  A. Watts.  On the Uniqueness of Equilibrium in Cournot Oligopoly and Other Games , 1996 .

[28]  Ehud Lehrer,et al.  Allocation processes in cooperative games , 2003, Int. J. Game Theory.

[29]  Imma Curiel,et al.  Cooperative game theory and applications , 1997 .

[30]  H. Moulin.  Equal or proportional division of a surplus, and other methods , 1987 .

[31]  Jens Leth Hougaard,et al.  The stand-alone test and decreasing serial cost sharing , 2000 .

[32]  J. Roemer.  Theories of Distributive Justice , 1997 .

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

[34]  Jens Leth Hougaard,et al.  Mixed serial cost sharing , 2001, Math. Soc. Sci..

[35]  Tatsuro Ichiishi,et al.  Super-modularity: Applications to convex games and to the greedy algorithm for LP , 1981 .

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

[37]  S. Tijs,et al.  Game theory and cost allocation problems , 1986 .

[38]  Jeroen Suijs.  Stochastic Cooperative Games , 2000 .

[39]  Judith Timmer,et al.  On three Shapley-like solutions for cooperative games with random payoffs , 2004, Int. J. Game Theory.

[40]  H. Moulin,et al.  Serial Cost Sharing , 1992 .

[41]  M. Angeles de Frutos.  Coalitional manipulations in a bankruptcy problem , 1999 .

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

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

[44]  Biung-Ghi Ju.  Manipulation via merging and splitting in claims problems , 2003 .

[45]  P. Moyes.  Some classes of functions that preserve the inequality and welfare orderings of income distributions , 1989 .

[46]  W. Thomson.  Fair Allocation Rules , 2011 .

[47]  J. Hougaard,et al.  Inequality preserving rationing , 2005 .

[48]  H. Peyton Young,et al.  On Dividing an Amount According to Individual Claims or Liabilities , 1987, Math. Oper. Res..

[49]  Y. Chun.  The proportional solution for rights problems , 1988 .

[50]  David Housman,et al.  Note Core and monotonic allocation methods , 1998, Int. J. Game Theory.

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

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

[53]  C.G.A.M. van den Nouweland,et al.  A game theoretic approach to problems in telecommunication , 1996 .

[54]  A. Rubinstein,et al.  Bargaining and Markets , 1991 .

[55]  S. C. Littlechild,et al.  Aircraft Landing Fees: A Game Theory Approach , 1977 .

[56]  William Thomson,et al.  Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update , 2015, Math. Soc. Sci..

[57]  D. Foley.  Resource allocation and the public sector , 1967 .