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2 edition of Shapley value in the non differentiable case found in the catalog.

Shapley value in the non differentiable case

Jean François Mertens

Shapley value in the non differentiable case

by Jean François Mertens

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  • 8 Currently reading

Published by Institute for Mathematical Studies in the Social Sciences, Stanford University in Stanford, Calif .
Written in English

    Subjects:
  • Game theory.

  • Edition Notes

    Other titlesShapely value in the non differentiable case
    Statementby Jean François Mertens.
    SeriesEconomics series / Institute for Mathematical Studies in the Social Sciences, Stanford University, Technical report / Institute for Mathematical Studies in the Social Sciences, Stanford University -- no. 417, Technical report (Stanford University. Institute for Mathematical Studies in the Social Sciences) -- no. 417., Economics series (Stanford University. Institute for Mathematical Studies in the Social Sciences)
    The Physical Object
    Pagination85 p. ;
    Number of Pages85
    ID Numbers
    Open LibraryOL22409011M

    ture regarding axioms for feature attribution for the case where there is a unique baseline reference input. Here in-tegrated gradients and Shapley values (as the generaliza-tion to discrete input) are the unique attribution functions for the stated set of axioms. Section 3 discusses the at-tribution problem for the case where one averages over. Mertens, J. () The Shapley value in the non differentiable case. International Journal of Game Theory, 17, 1 – Mirman, L. and Tauman, I. () Demand compatible equitable cost .

    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 non-atomic games, which are infinite-person games in which no individual player has significance. deed, the famous Banzhaf value,1 which is non-e¢ cient in general, may appropriately describe a case of strong "strategic risk aversion" (see Roth (b, )), where all players have an unduly pessimistic view of their bargaining abilities. In the context of simple (voting) games, the restriction of the Shapley and Banzhaf values to that.

    We derive versions of known results dealing with core, equilibria and Shapley-values of cooperative games in the case of cooperative fuzzy games, i.e., games defined on fuzzy subsets of the set of n players. A fuzzy coalition is an n-vector τ = (τ i) associating with each player i his “rate of participation” τ i ∈ [0, 1] in the fuzzy coalition and the real number v() is the.   However, a Shapley-value-based method is required for other (non-differentiable) model types. At Fiddler, we support both SHAP and IG. (Full disclosure: Ankur Taly, a co-author of IG, works at Fiddler, and is a co-author of this post.) Feel free .


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Shapley value in the non differentiable case by Jean François Mertens Download PDF EPUB FB2

THE SHAPLEY VALUE IN THE NON DIFFERENTIABLE CASE* by J. Mertens * Introduction.- " % In their book '4Values of Non Atomic Games4* Aumann and Shapley / define the Shapley value for non atomic games, and prove existence and uniqueness of it for a number of important spaces of games like pNA and bv'NA.

() The TU Value: The Non-differentiable Case. In: Mertens JF., Sorin S. (eds) Game-Theoretic Methods in General Equilibrium Analysis. NATO ASI Series (Series D: Behavioural and Social Sciences), vol Author: Jean-François Mertens. The appropriate — and most powerful — value in the non-differentiable case, introduced by Mertens () is considered; the existence and unicity of this value for monetary (i.e., transferable utility) markets was established by Mertens (), without any differentiability : Françoise Lefèvre.

MERTENS, Jean-François, "The Shapley value in the non differentiable case," CORE Discussion Papers RPUniversité catholique de Louvain, Center for Operations Research and Econometrics (CORE). The Shapley value in the non differentiable case. Jean-François Mertens ().

NoCORE Discussion Papers RP from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) Date: Note: In: International Journal of Game Theory, 17(1),References: Add references at CitEc Citations: View citations in EconPapers (2) Track citations Cited by: "The Shapley value in the non differentiable case," CORE Discussion Papers RPUniversité catholique de Louvain, Center for Operations Research and Econometrics (CORE).

Mertens, J F, " The Shapley Value in the Non Differentiable Case," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(1), pages This volume belongs to the series in Operations Research, and is devoted to the modern development and applications of the Shapley value—one of the most famous tools of the cooperative (non-antagonistic) game was introduced by Lloyd Shapley in (Shapley ), who together with his follower Alvin Roth (Roth ) won Nobel Prize in economics in The Shapley Value in the Non Differentiable Case International Journal of Game Theory,17, (1), View citations (8) See also Working Paper () A measure of aggregate power in organizations Journal of Economic Theory,43, (1), See also Working Paper () A counterexample to the folk theorem with discounting.

In contrast to the Aumann–Shapley value, however, the Weighted Aumann–Shapley value is well-defined even when the risk capital allocation function is non-differentiable. There is some literature on risk capital allocation in cases where the risk capital function is not differentiable.

Shapley Values. A prediction can be explained by assuming that each feature value of the instance is a “player” in a game where the prediction is the payout. Shapley values – a method from coalitional game theory – tells us how to fairly distribute the “payout” among the features.

for cooperative games, due to Lloyd S. Shapley (Shapley ()). In the first part, we will be looking at the transferable utility (TU) case, for which we will state the main theorem and study several examples. After-wards, we will extend the axiomatic construction to the non-transferable utility (NTU) case.

2 The Shapley Value in the TU Case. In finite transferable utility (TU) games, the Shapley value assigns a unique outcome to each game, which can be thought of as a sort of average or expected outcome or a priori measure of power. The Shapley value has a very broad spectrum of applications.

Book Description. Handbook of the Shapley Value contains 24 chapters and a foreword written by Alvin E. Roth, who was awarded the Nobel Memorial Prize in Economic Sciences jointly with Lloyd Shapley in The purpose of the book is to highlight a range of relevant insights into the Shapley value.

Every chapter has been written to honor Lloyd Shapley, who introduced this fascinating value in. We introduce a family of Capital allocation rules (C.A.R) based on the dual representation for risk measures and inspired to the Aumann-Shapley allocation principle.

These rules extend the one of Denault and Kalkbrener (for coherent risk measures) and the one of Tsanakas (convex case), to the case of non Gateaux differentiable risk measures. In their book Values of Non Atomic Games, Aumann and Shapley () define the Shapley value for non atomic games, and prove existence and uniqueness of it for a number of important spaces of.

The Shapley value is a solution concept in cooperative game was named in honor of Lloyd Shapley, who introduced it in and won the Nobel Prize in Economics for it in To each cooperative game it assigns a unique distribution (among the players) of a total surplus generated by the coalition of all players.

The Shapley value is characterized by a collection of desirable. Cost sharing: The nondifferentiable case.

In their book Values of Non Atomic Games, Aumann and Shapley () define the Shapley value for non atomic games, and prove existence and uniqueness. Now, quite clearly, the TU case isnot appropriate when weconsider economies or market games since itimplies the possibility ofinterpersonal comparisons ofutility.

A solution concept, similar tothe Shapley value but forthecaseof,non-transferable utility (NTU) games,wasprovided byHarsanyi [,].TheHarsanyi solution turned outto. The diagonal formula in the theory of nonatomic games expresses the idea that the Shapley value of each infinitesimal player is his marginal contribution to the worth of a “perfect sample” of the population of all players, when averaged over all possible sample sizes.

The concept of marginal contribution is most easily expressed in terms of derivatives; as a result, the diagonal formula. "The Shapley value in the non differentiable case", International Journal of Game The(CORE Reprint ). "Nondifferentiable TU markets: The value", in Alvin E. Roth (ed.), The Shapley Value: Essays in Honor of Lloyd S.

Shapley, Cambridge University Press,(CORE Reprint ). In game theory, the Shapley value, named in honour of Lloyd Shapley, who introduced it inis a solution concept in cooperative game theory.

To each cooperative game it assigns a unique distribution (among the players) of a total surplus generated by the coalition of all players. The Shapley value is characterized by a collection of desirable properties.2. Marginalism: the Shapley value can be defined as a function which uses only the marginal contributions of player i as the arguments.

Aumann–Shapley value. In their book, Lloyd Shapley and Robert Aumann extended the concept of the Shapley value to infinite games (defined with respect to a non-atomic measure), creating the diagonal.JEAN-FRANQOIS MERTENS This book presents a systematic exposition of the use of game theoretic methods in general equilibrium analysis.

Clearly the first such use was by Arrow and Debreu, with the "birth" of general equi­ librium theory itself, in using Nash's existence theorem (or a generalization) to prove the existence of a competitive equilibrium.