We consider environments in which agents can cooperate on multiple issues and externalities are present both within and across issues. We propose a way to extend (Shapley) values that have been put forward to deal with externalities within issues to games where there are externalities within and across issues. We characterize our proposal through axioms that extend the Shapley axioms to our mor...

The aim of the present paper is to study a one-point solution concept for bicooperative games. For these games introduced by Bilbao (Cooperative Games on Combinatorial Structures, 2000), we define a one-point solution called the Shapley value, since this value can be interpreted in a similar way to the classical Shapley value for cooperative games. The main result of the paper is an axiomatic c...

In fact the Shapley value is the unique efficient semivalue. This motivated Ruiz et al. to do additive efficient normalization for semivalues. In this paper, by matrix approach we derive the relationship between the additive efficient normalization of semivalues and the Shapley value. Based on the relationship, we axiomatize the additive efficient normalization of semivalues as the unique solut...

We consider the generalization of Shapley and Scarf’s (1974) [Shapley, L., Scarf’s, H., 1974. On cores and indivisibility. Journal of Mathematical Economics 1, 23–37.] model of trading indivisible objects (houses) to so-called multiple-type housing markets. We show that the prominent solution for these markets, the coordinate-wise core rule, is second-best incentive compatible. © 2007 Elsevier ...

The theory of non cooperative games with potential function was introduced by Monderer and Shapley in 1996. Such games have interesting properties, among which is the existence of equilibria in pure strategies. The paper by Monderer and Shapley has inspired many game theory researchers. In the present paper, many classes of multiobjective games with potential functions are studied. The notions ...

Marginanism and egalitarianism are two main standpoints in economics. The Shapley value has been characterized in many ways from the view of marginalism. In this paper, we characterize the Solidarity value with respect to the egalitarianism by three approaches applied to the Shapley value. We introduce a revised potential function and deduce the recursive formula of the Solidarity value. It is ...

A problem of identifying key drivers in customer satisfaction analysis is considered in relation to Kano theory on the relationship between product quality and customer satisfaction using tools from Cooperative Game Theory and Risk Analysis. We use Shapley Value and Attributable Risk techniques to identify priorities of key drivers of customer satisfaction, or key dissatisfiers and key enhancer...

A new coalitional value is proposed under the hypothesis of isolated unions. The main difference between this value and the Aumann–Drèze value is that the allocations within each union are not given by the Shapley value of the restricted game but proportionally to the Shapley value of the original game. Axiomatic characterizations of the new value, examples illustrating its application and a co...

Extending the problem of determining Ramsey numbers Erdős and Rogers introduced the following function. For given integers 2 ≤ s < t let fs,t(n) = min {max{|S| : S ⊆ V (H) and H[S] contains no Ks}} , where the minimum is taken over all Kt-free graphs H of order n. This function attracted a considerable amount of attention but despite that, the gap between the lower and upper bounds is still fai...