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  1. Jean Derks, Gerard van der Laan & Valery Vasil’ev (2010). On the Harsanyi Payoff Vectors and Harsanyi Imputations. Theory and Decision 68 (3):301-310.
    This article discusses the set of Harsanyi payoff vectors of a cooperative TU-game, also known as the Selectope. We reconsider some results on Harsanyi payoff vectors within a more general framework. First, an intuitive approach is used, showing that the set of Harsanyi payoff vectors is the core of an associated convex game. Next, the set of individual rational Harsanyi payoff vectors, the Harsanyi imputations in short, is considered. Existence conditions are provided, and if non-empty, we provide a description as (...)
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  2. P. Jean-Jacques Herings, Gerard Van Der Laan & Dolf Talman (2007). Socially Structured Games. Theory and Decision 62 (1):1-29.
    We generalize the concept of a cooperative non-transferable utility game by introducing a socially structured game. In a socially structured game every coalition of players can organize themselves according to one or more internal organizations to generate payoffs. Each admissible internal organization on a coalition yields a set of payoffs attainable by the members of this coalition. The strengths of the players within an internal organization depend on the structure of the internal organization and are represented by an exogenously given (...)
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  3. Gerard van Der Laan & René van Den Brink (2002). A Banzhaf Share Function for Cooperative Games in Coalition Structure. Theory and Decision 53 (1):61-86.
    A cooperative game with transferable utility–or simply a TU-game– describes a situation in which players can obtain certain payoffs by cooperation. A value function for these games assigns to every TU-game a distribution of payoffs over the players. Well-known solutions for TU-games are the Shapley and the Banzhaf value. An alternative type of solution is the concept of share function, which assigns to every player in a TU-game its share in the worth of the grand coalition. In this paper we (...)
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  4. Gerard van Der Laan & René van Den Brink (1998). Axiomatization of a Class of Share Functions for N-Person Games. Theory and Decision 44 (2):117-148.
    The Shapley value is the unique value defined on the class of cooperative games in characteristic function form which satisfies certain intuitively reasonable axioms. Alternatively, the Banzhaf value is the unique value satisfying a different set of axioms. The main drawback of the latter value is that it does not satisfy the efficiency axiom, so that the sum of the values assigned to the players does not need to be equal to the worth of the grand coalition. By definition, the (...)
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