We study the asymptotic nucleolus of a smooth and symmetric oligopoly with an atomless sector. We show that under appropriate assumptions, the asymptotic nucleolus of the TU market game coincides with the unique TU competitive payoff distribution x. This equivalence results from nucleolus of a finite game belonging to its core and the Aumann Core Equivalence, which holds for this economy due to...

Three service providers in competition, try to optimize their quality of service / content level and their service access price. But, they have to deal with uncertainty on the consumers’ preferences. To reduce their uncertainty, they have the opportunity to buy information and to build alliances. We determine the Shapley value which is a fair way to allocate the grand coalition’s revenue betwee...

We show that computing the Shapley value of minimum cost spanning tree games is #P-hard even if the cost functions are restricted to be {0, 1}-valued. The proof is by a reduction from counting the number of minimum 2-terminal vertex cuts of an undirected graph, which is #P-complete. We also investigate minimum cost spanning tree games whose Shapley values can be computed in polynomial time. We ...

Following Shapley (1976), we study the problem of the existence of a Nash Equilibrium (NE) in which each trading post is either active or “legitimately” inactive, and we call it a Shapley NE. We consider an example of an exchange economy, borrowed from Cordella and Gabszewicz (1998), which satisfies the assumptions of Dubey and Shubik (1978), and we show that the trivial equilibrium, the unique...

Let f be a finite variance function of d independent input variables. Sobol’ indices are used to measure the importance of input variables and subsets of them. They are based on a variance decomposition. A similar problem arises in economics, when the value produced through the joint efforts of a team is to be attributed to individual members of that team. The Shapley value is widely used to so...

The Multiple Partners assignment game is a natural extension of the Shapley and Shubik Assignment Game (Shapley and Shubik, 1972) to the case where the participants can form more than one partnership. In Sotomayor (1992) the existence of stable outcomes was proved. For the sake of completeness the proof is reproduced in Appendix I. In this paper we show that, as in the Assignment Game, stable p...

An extension of the Shapley value for games in partition function form is proposed in the paper. We introduce a version of the marginal contributions for environments with externalities. The dummy property related to it is defined. We adapt the system of axioms provided by Shapley (A value for n-Person games. In: Kuhn H, Tucker A (eds) Contributions to the theory of games II. Princeton Universi...

We examine general exchange markets with heterogenous indivisible goods, where each agent may be endowed with a set of indivisible goods, but there is no divisible good that could be used as a medium of exchange. Thus, our model is a generalization of the Shapley-Scarf housing market model, in which each agent owns one indivisible good. Our main result is a characterization of the set of group-...

Several authors, Brualdi and Scrimger [ 11, Folkman [2] and Woodall [5], have given necessary and sufficient conditions for an infinite family of sets with finitely many infinite members to have a transversal, generalising the well-known theorems of Hall [ 3 ] and Jung and Rado [4 1. In each case the proof of necessity is straightforward. Woodall’s proof of his theorem is one page long, and he ...

In this paper, we address the estimation of sensitivity indices called “Shapley effects.” These enable one to handle dependent input variables. The Shapley effects are generally...