179 research outputs found

    Comments on: Transversality of the Shapley value

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    It is a good tradition of TOP to invite experts in OR and game theory to write a surveyon a special topic. These papers are also interesting for readers who are not specialistsin the treated field but may have influence on their further research. For cooperativegame theory, in the past, there were survey papers on the compromise value (Tijsand Otten 1993) and on Operations Research Games (Borm et al. 2001), and thesepapers were frequently cited and inspired to new research. Now here is the paper byMoretti and Patrone on the Shapley value. As we can see in their list of references,in the fifty five years of the existence of the Shapley value, there have been not onlymany follow ups but also many surveys. This paper also gives a good survey of themany theoretical contributions in the past. But the feature of this survey is the eyefor applications. Many applications are well known just as the Shapley–Shubik indexin voting situations and the Baker–Thompson rule in landing fee problems, whereusers of a piece of the strip contribute equally to the costs. However, contributionsof the Shapley value in reliability theory and genetics are much less known. Theyare treated in this paper extensively, and they may inspire scientists in different otherdisciplines also to apply the Shapley value in new interactive situations. I think theauthors did an excellent job in writing a beautiful survey of topics around the Shapleyvalue and I expect that, inspired by this work, new practical situations will be foundwhere Shapleys ideas can again be useful

    Coordinating choice in partial cooperative equilibrium

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    In this paper we consider symmetric aggregative games and investigate partial cooperation between a portion of the players that sign a cooperative agreement and the rest of the players. Existence results of partial cooperative equilibria are obtained when the players who do not sign the agreement play a Nash equilibrium game having multiple solutions. Some applications in the supermodular case are discussed.Noncooperative games, cooperation, aggregative games, supermodular games.

    Partial Cooperation and Non-Signatories Multiple Decision

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    In this paper we investigate partial cooperation between a portion of the players and the rest of the players who do not cooperate and play a Nash game having multiple equilibria. Some properties of the partial cooperative equilibrium are studied and applied to a public goods situation.noncooperative games, cooperation, public goods games

    Convexity in stochastic cooperative situations

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    This paper introduces a new model concerning cooperative situations in which the payoffs are modeled by random variables. We analyze these situations by means of cooperative games with random payoffs. Special attention is paid to three types of convexity, namely coalitional-merge, individual-merge and marginal convexity. The relations between these types are studied and in particular, as opposed to their deterministic counterparts for TU games, we show that these three types of convexity are not equivalent. However, all types imply that the core of the game is nonempty. Sufficient conditions on the preferences are derived such that the Shapley value, defined as the average of the marginal vectors, is an element of the core of a convex game

    Convex games versus clan games

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    In this paper we provide characterizations of convex games and total clan games by using properties of their corresponding marginal games. We show that a "dualize and restrict" procedure transforms total clan games with zero worth for the clan into monotonic convex games. Furthermore, each monotonic convex game generates a total clan game with zero worth for the clan by a "dualize and extend" procedure. These procedures are also useful for relating core elements and elements of the Weber set of the corresponding games.convex games, core, dual games, marginal games, total clan games, Weber set

    A Dual Egalitarian Solution

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    In this note we introduce an egalitarian solution, called the dual egalitarian solution, that is the natural counterpart of the egalitarian solution of Dutta and Ray (1989). We prove, among others, that for a convex game the egalitarian solution coincides with the dual egalitarian solution for its dual concave game.Concave Games

    Shapley-like values for interval bankruptcy games

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    In this paper interval bankruptcy games arising from bankruptcy situations with interval claims are introduced. For this class of cooperative games two (marginal-based) Shapley-like values are considered and the relation between them is studied.
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