# The Shapley value in the non differentiate case

@article{Mertens1988TheSV, title={The Shapley value in the non differentiate case}, author={Jean-François Mertens}, journal={International Journal of Game Theory}, year={1988}, volume={17}, pages={1-65} }

The Shapley value is shown to exist even when there are essential non differentiabilities on the diagonal.

#### 49 Citations

The Shapley Value

- Economics
- 1994

The purpose of this chapter is to present an important solution concept for cooperative games, due to Lloyd S. Shapley (Shapley (1953)). In the first part, we will be looking at the transferable… Expand

Monotonicity and the Aumann-Shapley cost-sharing method in the discrete case

- Computer Science
- Eur. J. Oper. Res.
- 2014

We give an axiomatization of the Aumann–Shapley cost-sharing method in the discrete case by means of monotonicity and no merging or splitting (Sprumont, 2005). Monotonicity has not yet been employed… Expand

Power and public goods

- Economics
- 1987

Abstract A game-theoretic analysis using the Harsanyi-Shapley nontransferable utility value indicates that the choice of public goods in a democracy is not affected by who has voting rights. This is… Expand

On the Discrete Version of the Aumann-Shapley Cost-Sharing Method

- Economics
- 2005

Each agent in a finite set requests an integer quantity of an idiosyncratic good; the resulting total cost must be shared among the participating agents. The Aumann-Shapley prices are given by the… Expand

Values of perfectly competitive economies

- Economics
- 2002

Perfectly competitive economies are economic models with many agents, each of whom is relatively insignificant. This chapter studies the relations between the basic economic concept of competitive… Expand

On the symmetry axiom for values of nonatomic games

- Mathematics
- 1990

In this paper, a weaker version of the Symmetry Axiom on BV, and values on subspaces of BV are discussed. Included are several theorems and examples.

Payoffs in Nondifferentiable Perfectly Competitive TU Economies

- Economics, Computer Science
- J. Econ. Theory
- 2002

We show that a single-valued solution of non-atomic finite-type market games (or perfectly competitive TU economies underlying them) is uniquely determined as the Mertens value by four plausible… Expand

Addendum: The Shapley value of a perfectly competitive market may not exist

- Economics
- 1994

A counter-example for the existence of the Shapley value of non-differentiable perfectly competitive Walrasian (i.e., pure exchange) economies is given. The model used is that of a non-atomic… Expand

Cost sharing: the nondifferentiable case

- Mathematics
- 2001

We show existence and uniqueness of a cost allocation mechanism, satisfying standard axioms, on two classes of cost functions with major nondifferentiabilities. The first class consists of convex… Expand

Aumann-Shapley Pricing : A Reconsideration of the Discrete Case

- Economics
- 2004

We reconsider the following cost-sharing problem: agent i = 1, ...,n demands a quantity xi of good i; the corresponding total cost C(x1, ..., xn) must be shared among the n agents. The Aumann-Shapley… Expand

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