Convex Interval Games

In this paper, convex interval games are introduced and some characterizations are given. Some economic situations leading to convex interval games are discussed. The Weber set and the Shapley value are defined for a suitable class of interval games and their relations with the interval core for convex interval games are established. A square operator is introduced which allows us to obtain interval solutions starting from classical cooperative game theory solutions. It turns out that on the class of convex interval games the square Weber set coincides with the interval core.

[1]  Rodica Branzei,et al.  A New Characterization of Convex Games , 2004 .

[2]  R. Weiner.  Lecture Notes in Economics and Mathematical Systems , 1985 .

[3]  Donald B. Gillies,et al.  3. Solutions to General Non-Zero-Sum Games , 1959 .

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

[5]  Anja De Waegenaere,et al.  Cooperative games with stochastic payoffs , 1999, Eur. J. Oper. Res..

[6]  R. Branzei,et al.  Bankruptcy problems with interval uncertainty , 2008 .

[7]  R. Branzei,et al.  Cores and Stable Sets for Interval-Valued Games , 2008 .

[8]  J. Potters,et al.  Large Cores and Exactness , 1999 .

[9]  Silvia Miquel,et al.  Cooperation under interval uncertainty , 2008, Math. Methods Oper. Res..

[10]  Stef Tijs,et al.  Models in Cooperative Game Theory , 2008 .

[11]  Juan Enrique Martínez-Legaz,et al.  Some Characterizations of Convex Games , 2006 .

[12]  Judith Timmer,et al.  Convexity in Stochastic Cooperative Situations , 2005, IGTR.

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

[14]  Stef Tijs,et al.  Bankruptcy games , 1987, Z. Oper. Research.

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

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

[17]  Rodica Branzei,et al.  How to Handle Interval solutions for Cooperative Interval Games , 2010, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[18]  Herbert Hamers,et al.  Operations research games: A survey , 2001 .

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

[20]  Juan-Enrique Martínez-Legaz.  Two Remarks on Totally Balanced Games , 1996 .

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

[22]  Peter E. Kennedy,et al.  F Versus T Tests for Unit Roots , 2001 .

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

[24]  Hao Sun.  Contributions to set game theory , 2003 .

[25]  Irinel Dragan,et al.  Superadditivity for solutions of coalitional games , 1989 .

[26]  H. Moulin.  Axioms of Cooperative Decision Making , 1988 .

[27]  R. Branzei,et al.  Some Characterizations of Convex Interval Games , 2008 .

[28]  S. C. Littlechild,et al.  A further note on the nucleoous of the “airport game” , 1976 .

[29]  Rodica Branzei,et al.  Cooperative Interval Games Arising from Airport Situations with Interval Data , 2008 .

[30]  T. Driessen.  Cooperative Games, Solutions and Applications , 1988 .

[31]  R. Branzei,et al.  Models in cooperative game theory : crisp, fuzzy, and multi-choice games , 2005 .

[32]  Abraham Charnes,et al.  Prior Solutions: Extensions of Convex Nucleus Solutions to Chance-Constrained Games. , 1973 .

[33]  Rodica Branzei,et al.  The interval Shapley value: an axiomatization , 2010, Central Eur. J. Oper. Res..