The compromise value for NTU-games

The compromise value is introduced as a single-valued solution concept for NTU-games. It is shown that the compromise value coincides with the -value for TU-games and with the Kalai-Smorodinsky solution for bargaining problems. In addition the axiomatic characterizations of both the two-person Kalai-Smorodinsky solution and the -value can be extended to the compromise value for large classes of NTU-games.We also present an alternative NTU-extension of the TU -value (called the NTU -value) which coincides with the Nash solution for two-person bargaining problems. The definition of the NTU -value is analogous to that of the Shapley NTU-value.     

Cooperative interval games: a survey

The (re)distribution of collective gains and costs is a central question for individuals and organizations contemplating cooperation under uncertainty. The theory of cooperative interval games provides a new game theoretical angle and suitable tools for answering this question. This survey aims to briefly present the state-of-the-art in this young field of research, discusses how the model of cooperative interval games extends the cooperative game theory literature, and reviews its existing and potential applications in economic and operations research situations with interval data.     

Restricted component additive games

Curiel, Potters, Prasad, Tijs and Veltman (1993) introduced component additive games which are cooperative TU games that arise by imposing an order on the player set. Further, they introduced the -rule which allocates a core element to each component additive game.In this paper we consider the class of restricted component additive games that arise by restricting the attention to head-tail coalitions. The extreme points of the corresponding restricted core are characterized. Further, it is shown that the -rule is the barycenter of the corresponding restricted core and that the -rule coincides with the nucleolus of this restricted game.     

Equilibria for Pooling Situations

This paper deals with pooling situations, which can be considered as exchange economies with indivisible goods and money, and two related cooperative games which we refer to as pooling games with individual rights and pooling games without individual rights. It is shown that the classes of pooling games without individual rights and transportation games coincide and are contained in the class of pooling games with individual rights. With tools from discrete convexity theory, it is proved that competitive equilibria for pooling situations exist. As a consequence, an alternative proof of the nonemptiness of the core of pooling games is provided.     

On pure equilibria for bimatrix games

In Shapley (1964) several conditions are given for the existence of pure saddlepoints for a matrix game. In this paper we show that only a few of these conditions, when translated to the situation of a bimatrix game guarantee the existence of pure equilibria. Further, we associate with a bimatrix game a directed graph as well as a so-called binary game. If this graph has no cycles, then the bimatrix game in question has a pure equilibrium. It is shown that the binary game for a bimatrix game without a pure equilibrium possesses a fundamental subgame, which can be characterized by means of minimal cycles.     

A symmetrization for finite two-person games

The symmetrization method of Gale, Kuhn and Tucker for matrix games is extended for bimatrix games. It is shown that the equilibria of a bimatrix game and its symmetrization correspond two by two. A similar result is found with respect to quasi-strong, regular and perfect equilibria.     

Compromise values in cooperative game theory

Summary The aim of this paper is to give a survey on several well-known compromise values in cooperative game theory and its applications. Special attention is paid to the τ-value for TU-games, the Raiffa-Kalai-Smorodinsky solution for bargaining problems, and the compromise value for NTU-games.     

A fluorescence approach to investigate repartitioning of coalescing agents in acrylic polymer emulsions

Repartitioning of co-solvents between particles of latex emulsions was investigated by means of a fluorescence method based on the detection of the amount of co-solvent via the solvatochromic shift of the emission maximum of a fluorescent probe, copolymerized at a low concentration. Complete repartitioning of co-solvents between particles of latex materials with a low T _g (ca. 25 °C) occurred within minutes. For a hydrophilic latex with a T _g of 68 °C, equilibration was achieved within an hour. Repartitioning was faster for more hydrophobic co-solvents. For a hydrophobic latex of similar T _g , co-solvent repartitioning took place on the same time scale, but complete equilibration was not reached. Possibly, there is an additional slow component in the repartitioning, or the prolonged presence of co-solvent causes a structural change in the latex particles that affects the outcome of the experiment.