### A bargaining procedure with offer-dependent breakdown probabilities.

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A probabilistic communication structure considers the setting with communication restrictions in which each pair of players has a probability to communicate directly. In this paper, we consider a more general framework, called a probabilistic communication structure with fuzzy coalition, that allows any player to have a participation degree to cooperate within a coalition. A maximal product spanning tree, indicating a way of the greatest possibility to communicate among the players, is introduced...

In the class of complete games, the Shapley index of power is the characteristic invariant of the group of automorphisms, for these are exactly the permutations of players preserving the index.

In Benaïm and Ben Arous (2003) is solved a multi-armed bandit problem arising in the theory of learning in games. We propose a short and elementary proof of this result based on a variant of the Kronecker lemma.

This paper deals with cooperative games with $n$ players and $r$ alternatives which are called multi-alternative games. In the conventional multi-alternative games initiated by Bolger, each player can choose any alternative with equal possibilities. In actual social life, there exist situations in which players have some restrictions on their choice of alternatives. Considering such situations, we study restricted multi-alternative games. A value for a given game is proposed.

The fuzzy coalition game theory brings a more realistic tools for the mathematical modelling of the negotiation process and its results. In this paper we limit our attention to the fuzzy extension of the simple model of coalition games with side-payments, and in the frame of this model we study one of the elementary concepts of the coalition game theory, namely its “additivities”, i. e., superadditivity, subadditivity and additivity in the strict sense. In the deterministic game theory these additivites...

One of the possible models of fuzzification of non-transferable utility (NTU) coalitional games was extensively treated in [4]. In this paper, we suggest an alternative structure of fuzzification of the NTU games, where for every coalition a fuzzy class of (generally crisp) sets of its admissible pay-off vectors is considered. It is shown that this model of a fuzzy coalitional game can be represented by a fuzzy class of deterministic NTU games, and its basic concepts like the superadditivity or...

Some real situations which may be described as weighted majority games can be modified when some players increase or decrease their weights and/or the quota is modified. Nevertheless, some of these modifications do not change the game. In the present work we shall estimate the maximal percentage variations in the weights and the quota which may be allowed without changing the game (amplitude). For this purpose we have to use strict representations of weighted majority games.

The aspiration core of a TU game was introduced by Bennett [1] as a payoff vector which is undominated and achievable in the sense that each player belongs to a coalition which can obtain the specified payoff for its members, and which minimizes the distance to the set of aggregate feasible payoffs among all such payoff vectors. In the paper a set of axioms is proposed which characterize the aspiration core, which may be considered as an extension of the core to a much larger set of games. The axioms...

We propose new systems of axioms which characterize four types of values of cooperative games: the Banzhaf value, the Deegan-Packel value, the least square prenucleolus and the least square nucleolus. The common element used in these axiomatizations is a fairness property. It requires that if to a cooperative game we add another game in which two given players are symmetric, then their payoffs change by the same amount. In our analysis we will use an idea applied by R. van den Brink (2001) to obtain...

The paper deals with the concept of coalitional preferences in the group decision-making situations in which the agents and coalitions have only vague idea about the comparative acceptability of particular outcomes. The coalitional games with vague utilities (see, e. g., [6]) can serve for a good example when some types of the game solutions (e. g., the von Neumann– Morgenstern one) are to be extended to the fuzzy game case. In this paper, we consider the fuzzy analogies of coalitional preferences...

A cooperative game is defined as a set of players and a cost function. The distribution of the whole cost between the players can be done using the core concept, that is the set of all undominated cost allocations which prevent players from grouping. In this paper we study a game whose cost function comes from the optimal solution of a linear integer covering problem. We give necessary and sufficient conditions for the core to be nonempty and characterize its allocations using linear programming...