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...

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...

The principle of differential marginality for cooperative games states that the differential of two players’ payoffs does not change when the differential of these players’ productivities does not change. Together with two standard properties, efficiency and the null player property, differential marginality characterizes the Shapley value. For games that contain more than two players, we show ...

We prove that the Shapley value of every two-sided exact assignment game lies in the core of the game.

This article describes the basic elements of the cooperative approach to game theory, one of the two counterparts of the discipline. After the presentation of some basic definitions, the focus will be on the core and the Shapley value, two of the most central solution concepts in cooperative game theory. JEL classification: C7.

Nota: this compilation of various results has been intended primarily for my personal use, hence its very rough form. It is just a quick reference compilation of results. It is far to be complete, and does not intend to be so especially for references, and I update it from time to time. All comments, discovered mistakes, etc. are welcome. Please be kind enough to cite it in references if you us...

We present and study the Contribution-Selection algorithm (CSA), a novel algorithm for feature selection. The algorithm is based on the Multiperturbation Shapley Analysis, a framework which relies on game theory to estimate usefulness. The algorithm iteratively estimates the usefulness of features and selects them accordingly, using either forward selection or backward elimination. Empirical co...

We investigate the distribution of the well-studied Shapley–Shubik values in weighted voting games where the agents are stochastically determined. The Shapley-Shubik value measures the voting power of an agent, in typical collective decision making systems. While easy to estimate empirically given the parameters of a weighted voting game, the Shapley values are notoriously hard to reason about ...

The Shapley value provides a fair method for the division of value in coalitional games. Motivated by the application of crowdsourcing for the collection of suitable labels and features for regression and classification tasks, we develop a method to approximate the Shapley value by identifying a suitable decomposition into multiple issues, with the decomposition computed by applying a graph par...