In this paper we prove the existence and uniqueness of a solution concept for n-person games with fuzzy coalitions, which we call the Shapley mapping. The Shapley mapping, when it exists, associates to each fuzzy coalition in the game an allocation of the coalitional worth satisfying the efficiency, the symmetry, and the null-player conditions. It determines a “cumulative value” that is the “su...

where W(y, t) is a quadratic form whose coefficients depend upon those elements &„•(<) of B(t) for which i < j, i, j = 1, 2, • • • n. Since these elements can always be made sufficiently small by a transformation with constant coefficients (which will not affect stability properties) the derivative dV/dt will be a negative definite quadratic form. Hence the trivial solution y(t) = 0 of (2) is a...

A partially de ned cooperative game is a coalition function form game in which some of the coalitional worths are not known. An application would be cost allocation of a joint project among so many players that the determination of all coalitional worths is prohibitive. This paper generalizes the concept of the Shapley value for cooperative games to the class of partially de ned cooperative gam...

We propose a simple mechanism to determine how the surplus generated by cooperation is to be shared in zero-monotonic environments with transferable utility. The mechanism consists of a bidding stage followed by a proposal stage. We show that the subgame perfect equilibrium outcomes of this mechanism coincide with the vector of the Shapley value payoffs. We extend our results to implement the w...

In an argumentation setting, a semantics evaluates the overall acceptability of arguments. Consequently, it reveals the global loss incurred by each argument due to attacks. However, it does not say anything on the contribution of each attack to that loss. This paper introduces the novel concept of contribution measure for evaluating those contributions. It starts by defining a set of axioms th...

The objective of this paper is to give the prospective outcome or "prospect" of a negotiation when the players’ value can only be realized if a certain threshold is reached. Thresholds can be of different forms such as a certain number of players, a certain coalition of players or a certain total level of contribution. A value is proposed, which is defined for a given game and a given threshold...

Cooperation among genetically unrelated individuals is commonly explained by the potential for future reciprocity or by the risk of being punished by group members. However, unconditional altruism is more difficult to explain. We demonstrate that unconditional altruism can evolve as a costly signal of individual quality (i.e. a handicap) as a consequence of reciprocal altruism. This is because ...

The weighted value was introduced by Shapley in 1953 as an asymmetric version of his value. Since then several axiomatizations have been proposed including one by Shapley in 1981 specifically addressed to cost allocation, a context in which weights appear naturally. It was at the occasion of a comment in which only the axioms were stated. The present paper offers a proof of Shapley's statement ...

Starting from her home, a service provider visits several customers, following a predetermined route, and returns home after all customers are visited. The problem is to …nd a fair allocation of the total cost of this tour among the customers served. A transferableutility cooperative game can be associated with this cost allocation problem. We introduce a new class of games, which we refer as t...

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