The Shapley value in the non differentiate case

  title={The Shapley value in the non differentiate case},
  author={Jean-François Mertens},
  journal={International Journal of Game Theory},
  • J. Mertens
  • Published 1988
  • Economics
  • International Journal of Game Theory
The Shapley value is shown to exist even when there are essential non differentiabilities on the diagonal. 

The Shapley Value

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

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

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

Payoffs in Nondifferentiable Perfectly Competitive TU Economies

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

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

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

Cost sharing: the nondifferentiable case

Aumann-Shapley Pricing : A Reconsideration of the Discrete Case

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

The TU Value: The Non-differentiable Case

A cooperative game υ (in characteristic function form) is defined by: (i) A set I of players. (ii) A sub-algebra C of the boolean algebra of subsets of I. The elements of C are



Value on a class of non-differentiable market games

We prove the existence of a (unique) Aumann-Shapley value on the space on non-atomic gamesQn generated byn-handed glove games. (These are the minima ofn non-atomic mutually singular probability

Measure-Based Values of Market Games

  • S. Hart
  • Economics
    Math. Oper. Res.
  • 1980
The idea of “marginal contribution” is best captured in the game theoretic concept of value. The relation between it and the usual economic equilibrium can be stated as the following Value Principle:

Values of Non-Atomic Games

The "Shapley value" of a finite multi- person game associates to each player the amount he should be willing to pay to participate. This book extends the value concept to certain classes of

Values and Derivatives

An averaging process is used to reinterpret and then prove the diagonal formula for much larger spaces of games, including spaces in which the games cannot be considered differentiable and may even have jumps (e.g., voting games).