Compatibilité entre conduites sociales réelles dans des groupes et les représentations symboliques de ces groupes : un essai de formalisation mathématique
Compromise in Cooperative Game and the
Contractual -core and equilibrium allocations.
Convex interval games.
Convexity of production, common pool and oligopoly games: a survey
The paper surveys a uniform proof technique of the convexity property for three different cooperative TU games arising from three different economical settings. The production economy, common pool situation and oligopoly framework involve a cost function, but different production functions. Each of the three corresponding game theoretic models refers to some maximization problem described by optimizing a certain net profit function over all feasible production levels. The current mathematical proof...
Cooperación y defensa.
Se aplican conceptos y técnicas de la teoría de juegos cooperativos a problemas de decisión que afectan a la política de Defensa del país. El análisis permite evaluar las propuestas sobre procedimientos de votación cualificada presentadas al Consejo Europeo en la cumbre de Maastricht de diciembre de 1991. Se ponen así de manifiesto las implicaciones que supondría para la posición estratégica de España la inédita capacidad operativa concedida a la Comunidad por el tratado de unión política.
Cooperative fuzzy games extended from ordinary cooperative games with restrictions on coalitions
Cooperative games are very useful in considering profit allocation among multiple decision makers who cooperate with each other. In order to deal with cooperative games in practical situations, however, we have to deal with two additional factors. One is some restrictions on coalitions. This first factor has been taken into consideration through feasibility of coalitions. The other is partial cooperation of players. In order to describe this second factor, we consider fuzzy coalitions which permit...
Cooperative games with a simplicial core.
Cooperative networks games with elastic demands
We present here a pricing model which is an extension of the cooperative game concept and which includes a notion of elastic demand. We present some existence results as well as an algorithm, and we conclude by discussing a specific problem related to network pricing.
Core and Coalition - Power in a Public Good Economy
Disjointness of fuzzy coalitions
The cooperative games with fuzzy coalitions in which some players act in a coalition only with a fraction of their total “power” (endeavor, investments, material, etc.) or in which they can distribute their “power” in more coalitions, are connected with some formal or interpretational problems. Some of these problems can be avoided if we interpret each fuzzy coalition as a fuzzy class of crisp coalitions, as shown by Mareš and Vlach in [9,10,11]. The relation between this model of fuzziness and...
Division schemes under uncertainty of claims
In some economic or social division problems, we may encounter uncertainty of claims, that is, a certain amount of estate has to be divided among some claimants who have individual claims on the estate, and the corresponding claim of each claimant can vary within a closed interval or fuzzy interval. In this paper, we classify the division problems under uncertainty of claims into three subclasses and present several division schemes from the perspective of axiomatizations, which are consistent with...
Dynamic solution of general coalition-games
Ein Beitrag zu den Kooperativen N-Personen-Spielen Ohne Seitenxahlungen. Ein Beispiel fuer die Machtverteilung in einer Aktiengesellschaft
El potencial de Hart y Mas-Colell para juegos restringidos por grafos.
This paper analyzes a model of formation of connected coalitions in a cooperative game. This model is a communication situation, and the Shapley value of this graph-restricted game is the Myerson value. The potential function for cooperative games was defined by Hart and Mas-Colell, and Winter showed that the Myerson value admits a potential function. We study a recursive procedure for computing the potential of the Myerson value. In section 3, we use the Myerson value for measuring voting power...
Existence of equilibria in finitely additive nonatomic coalition production economies.
Fair majorities in proportional voting
In parliaments elected by proportional systems the seats are allocated to the elected political parties roughly proportionally to the shares of votes for the party lists. Assuming that members of the parliament representing the same party are voting together, it has sense to require that distribution of the influence of the parties in parliamentary decision making is proportional to the distribution of seats. There exist measures (so called voting power indices) reflecting an ability of each party...
Fast computation of the leastcore and prenucleolus of cooperative games
The computation of leastcore and prenucleolus is an efficient way of allocating a common resource among n players. It has, however, the drawback being a linear programming problem with 2n - 2 constraints. In this paper we show how, in the case of convex production games, generate constraints by solving small size linear programming problems, with both continuous and integer variables. The approach is extended to games with symmetries (identical players), and to games with partially continuous...
Four different approaches to the normalized Banzhaf values of games with a priori unions
Applying the Owen construction of value of games with a priori unions to the normalized Banzhaf value gives a new type of the normalized Banzhaf value for games with a priori unions. Using a simple example of a four-person voting game with a priori unions, it is shown that this value is different from those known in the literature: the normalized Owen-Banzhaf value, the Banzhaf share function defined by van der Laan and van den Brink and the Banzhaf index for simple games with a priori unions introduced...
Fuzzy coalitional structures (alternatives).
The uncertainty of expectations and vagueness of the interests belong to natural components of cooperative situations, in general. Therefore, some kind of formalization of uncertainty and vagueness should be included in realistic models of cooperative behaviour. This paper attempts to contribute to the endeavour of designing a universal model of vagueness in cooperative situations. Namely, some initial auxiliary steps toward the development of such a model are described. We use the concept of fuzzy...