Coalitional values for cooperative games withr alternatives

In this paper we consider games withn players andr alternatives. In these games the worth of a coalition depends not only on that coalition, but also on the organization of the other players in the game. We propose two coalitional values that are extensions of the Owen value (1977). We give some relations with the Owen value and an axiomatic characterization of each value introduced in this work. Finally, we compare both values. This research has been supported partially by U.P.V./E.H.U. research project 035.321-HB048/97, and the DGES of MEC project PB96-0247.     

Axiomatic characterizations of generalized values

In the framework of cooperative game theory, the concept of generalized value, which is an extension of that of value, has been recently proposed to measure the overall influence of coalitions in games. Axiomatizations of two classes of generalized values, namely probabilistic generalized values and generalized semivalues, which extend probabilistic values and semivalues, respectively, are first proposed. The axioms we utilize are based on natural extensions of axioms involved in the axiomatizations of values. In the second half of the paper, special instances of generalized semivalues are also axiomatized.     

Order monotonic solutions for generalized characteristic functions

Generalized characteristic functions extend characteristic functions of ‘classical’ TU-games by assigning a real number to every ordered coalition being a permutation of any subset of the player set. Such generalized characteristic functions can be applied when the earnings or costs of cooperation among a set of players depend on the order in which the players enter a coalition.     

Weighted shapley values for games in generalized characteristic function form

We study the family of weighted Shapley values for games in generalized characteristic function form. These values are defined and characterized.     

Weighted Banzhaf values

The family of weighted Banzhaf values for cooperativen-person TU-games is studied. First we introduce the weighted Banzhaf value for an exogenously given vector of positive weights of the players. Then we give an axiomatic characterization of the class of all possible weighted Banzhaf values.     

Linear values for interior operator games

Interior operator games were introduced by Bilbao et al. (2005) as additive games restricted by antimatroids. In that paper several interesting cooperative games were shown as examples of interior operator games. The antimatroid is a known combinatorial structure which represents, in the game theory context, a dependence system among the players. The aim of this paper is to study a family of values which are linear functions and satisfy reasonable conditions for interior operator games. Two classes of these values are considered assuming particular properties.     

Arithmetic of Levitan's generalized characteristic functions

Some properties are stated for functions of the form, where is a distribution on the halfline [0,).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 61, pp. 56–58, 1976.I thank Prof. I. V. Ostrovskii for suggesting this problem and for his support.     

Coalitional games: Monotonicity and core

We characterize a monotonic core solution defined on the class of veto balanced games. We also discuss what restricted versions of monotonicity are possible when selecting core allocations. We introduce a family of monotonic core solutions for veto balanced games and we show that, in general, the per capita nucleolus is not monotonic.     

A core-allocation family for generalized holding cost games

Inventory situations, introduced in Meca et al. (Eur J Oper Res 156: 127–139, 2004), study how a collective of firms can minimize its joint inventory cost by means of co-operation. Depending on the information revealed by the individual firms, they analyze two related cooperative TU games: inventory cost games and holding cost games, and focus on proportional division mechanisms to share the joint cost. In this paper we introduce a new class of inventory games: generalized holding cost games, which extends the class of holding cost games. It turns out that generalized holding cost games are totally balanced.We then focus on the study of a core-allocation family which is called N-rational solution family.It is proved that a particular relation of inclusion exists between the former and the core. In addition, an N-rational solution called minimum square proportional ruleis studied. This work was partially supported by the Spanish Ministry of Education and Science, and the Generalitat Valenciana (grants MTM2005-09184-C02-02, CSD2006-00032, ACOMP06/040). The author thanks Javier Toledo, Josefa Cá novas, and two anonymous referees for helpful comments.     

On generating functions of multiple zeta values and generalized hypergeometric functions

Generating functions for sums of certain multiple zeta values with fixed weight, depth and i-heights are discussed. The functions are systematically expressed in terms of generalized hypergeometric functions. The expressions reproduce several known formulas for multiple zeta values as applications.     

A Coalitional Power Value for Set Games

We propose the concept of a coalitional power value for set games, and present its axiomatic characterization of global efficiency, equal treatment property and coalitional power monotonicity. The coalitional power value is a generalization of the marginalistic value introduced by Aarts et al.     

Methods for comparison of coalition influence on games in characteristic function form and their interrelationships

This paper extends two existent methods, called the blockability relation and the viability relation, for simple games to compare influence of coalitions, to those for games in characteristic function form, and shows that the newly defined relations satisfy transitivity and completeness. It is shown in this paper that for every game in characteristic function form the blockability relation and the viability relation have a complementary interrelationship.     

On the bargaining set, kernel and core of superadditive games

We prove that for superadditive games a necessary and sufficient condition for the bargaining set to coincide with the core is that the monotonic cover of the excess game induced by a payoff be balanced for each imputation in the bargaining set. We present some new results obtained by verifying this condition for specific classes of games. For N-zero-monotonic games we show that the same condition required at each kernel element is also necessary and sufficient for the kernel to be contained in the core. We also give examples showing that to maintain these characterizations, the respective assumptions on the games cannot be lifted. Received: March 1998/Revised version: December 1998     

Mixing weighted values of non-atomic games

Weighted values of non-atomic games were introduced by Hart and Monderer (1997). They study these values by using two approaches: the potential approach and the asymptotic approach. In this study we develop the random order approach (the mixing value, Aumann and Shapley, 1974) to weighted values and prove that these values coincide with the asymptotic weighted values of Hart and Monderer in pNA. Received April 1995/Revised version May 1996/ Final version October 1997     

An alternative characterization of the weighted Banzhaf value

We provide a new characterization of the weighted Banzhaf value derived from some postulates in a recent paper by Radzik, Nowak and Driessen [7]. Our approach owes much to the work by Lehrer [4] on the classical Banzhaf value based on the idea of amalgamation of pairs of players and an induction construction of the value. Compared with the approach in [7] we consider two new postulates: a weighted version of Lehrer’s “2-efficiency axiom” [4] and a generalized “null player out” property studied in terms of symmetric games by Derks and Haller [2]. Received: December 1997/final version: October 1999     

Consistent values and the core in continuum market games with two types of players

The consistent value is an extension of the Shapley value to the class of games with non-transferable utility.? In this paper, the consistent value will be characterized for market games with a continuum of players of two types. We will show that for such games the consistent value need not belong to the core, and provide conditions under which there is equivalence between the two concepts. Received: October 1998 RID="*" ID="*"  This thesis was completed under the supervision of Professor Sergiu Hart, The Center for Rationality and Interactive Decision Theory, Department of Mathematics, Department of Economics, The Hebrew University of Jerusalem. I would like to thank Professor Hart for introducing me to this area of research, for his help and guidance, and, especially, for all his patience.? I would also like to thank Michael Borns for improving the style, and an anonymous referee for helpful comments.     

Certain values of Hecke L-functions and generalized hypergeometric functions

We compare two calculations due to Bloch and the author of the regulator of an elliptic curve with complex multiplication which is a quotient of a Fermat curve, and express the special value of its L-function at s=0 in terms of special values of generalized hypergeometric functions.     

A note on sign symmetry for a subclass of efficient,symmetric, and linear values

Symmetry requires that equally productive players should get the same payoff. Sign symmetry is a considerable weakening of symmetry, which requires equally productive players' payoffs to have the same sign. In this note, we apply sign symmetry, as a substitute of symmetry to characterize a subclass of efficient, symmetric, and linear values.     

On the core of cooperative queueing games

We consider a class of cooperative games for managing several canonical queueing systems. When cooperating parties invest optimally in common capacity or choose the optimal amount of demand to serve, cooperation leads to “single-attribute” games whose characteristic function is embedded in a one-dimensional function. We show that when and only when the latter function is elastic will all embedded games have a non-empty core, and the core contains a population monotonic allocation. We present sufficient conditions for this property to be satisfied. Our analysis reveals that in most Erlang B and Erlang C queueing systems, the games under our consideration have a non-empty core, but there are exceptions, which we illustrate through a counterexample.