Narrow Results

In economic allocation problems, egalitarianism and marginalism are two major thoughts to distribute the benefits of cooperation. The α-CIS value reconciles the two thoughts in some variable extent by a parameter α ∈ [0, 1]. The α-CIS value is the center of gravity of the corresponding α-imputation set given the α-imputation set is nonempty. From the cooperative perspective, we present several axiomatizations of the α-CIS value using α-individual rationality or α-dummifying player property. Finally, we provide a noncooperative interpretation of the α-CIS value by a bidding mechanism.

In order to study the axiomatization of the if-then-else construct over possibly non-halting programs and tests, this paper introduces the notion of $C$-sets by considering the tests from an abstract $C$-algebra. When the $C$-algebra is an ada, the axiomatization is shown to be complete by obtaining a subdirect representation of $C$-sets. Further, this paper considers the equality test with the if-then-else construct and gives a complete axiomatization through the notion of agreeable $C$-sets.

In a recent paper [International Journal of Uncertainty, Fuzziness, and Knowledge-Based Systems 8:611–618], Yager & Kreinovich characterize a certain proportional division rule in terms of the three axioms (1) symmetry, (2) participant mergability, and (3) continuity. This technical note tightens their characterization: The proportional division rule is already fully characterized by the first two axioms (1) symmetry and (2) participant mergability.

We study the so-called signed discrete Choquet integral (also called non-monotonic discrete Choquet integral) regarded as the Lovász extension of a pseudo-Boolean function which vanishes at the origin. We present axiomatizations of this generalized Choquet integral, given in terms of certain functional equations, as well as by necessary and sufficient conditions which reveal desirable properties in aggregation theory.

In this paper we consider a multicriteria aggregation model where local utility functions of different sorts are aggregated using Sugeno integrals, and which we refer to as Sugeno utility functions. We propose a general approach to study such functions via the notion of pseudo-Sugeno integral (or, equivalently, pseudo-polynomial function), which naturally generalizes that of Sugeno integral, and provide several axiomatizations for this class of functions.

Moreover, we address and solve the problem of factorizing a Sugeno utility function as a composition q(φ₁(x₁),…,φ_n(x_n)) of a Sugeno integral q with local utility functions φ_i, if such a factorization exists.

In this paper, we provide alternative axioms and related axiomatizations of the Shapley value under interval uncertainty.

In this paper we revise the axiomatic foundations and meaning of semivalues as measures of power on the domain of simple games, when these are interpreted as models of voting procedures. In this context we characterize the family of preferences on roles in voting procedures they represent, and each of them in particular. To this end we first characterize the family of semivalues and each of them in particular up to the choice of a zero and a unit of scale. As a result a reinterpretation of semivalues as a class of power indices is proposed and critically discussed.

In this paper we propose an extension of the core of NTU games from its domain to a larger set of games satisfying a few conditions of well-behavedness. The solution concept is a rather straightforward generalization of the extended core of TU games introduced by Gomez [2003] and is shown to have similar properties. Also, a set of axioms for solutions of NTU games is presented which characterizes the extended core.

We study a non-cooperative model of unilateral network formation. Derks et al. [2008b] prove the existence of local-Nash and global-Nash networks for games with payoff functions that satisfy a framework of axiomatic properties. These properties are inspired by the one-way flow model, which is characterized by the following payoff structure. Each agent pays a cost for each formed link and receives profits from being connect to other agents. In this paper we fully characterize the payoff functions in the one-way flow model that satisfy all properties. We show that under certain conditions, payoff functions with heterogeneous link costs and heterogeneous profits satisfy all properties for which the existence of local-Nash networks is proved. Furthermore, we show that all payoff functions with owner-homogeneous link costs and heterogeneous profits satisfy all properties, and therefore imply the existence of global-Nash networks.

We provide axiomatic characterizations of the solutions of transferable utility (TU) games on the fixed player set, where at least three players exist. We introduce two axioms on players’ nullification. One axiom requires that the difference between the effect of a player’s nullification on the nullified player and on the others is relatively constant if all but one players are null players. Another axiom requires that a player’s nullification affects equally all of the other players. These two axioms characterize the set of all affine combinations of the equal surplus division and equal division values, together with the two basic axioms of efficiency and null game. By replacing the first axiom on players’ nullification with appropriate monotonicity axioms, we narrow down the solutions to the set of all convex combinations of the two values, or to each of the two values.

We introduce the concept of associativity for string functions, where a string function is a unary operation on the set of strings over a given alphabet. We discuss this new property and describe certain classes of associative string functions. We also characterize the recently introduced preassociative functions as compositions of associative string functions with injective unary maps. Finally, we provide descriptions of the classes of associative and preassociative functions which depend only on the length of the input.