Aggregate monotonic stable single-valued solutions for cooperative games

This article considers single-valued solutions of transferable utility cooperative games that satisfy core selection and aggregate monotonicity, defined either on the set of all games, G ^N , or on the set of essential games, E ^N (those with a non-empty imputation set). The main result is that for an arbitrary set of players, core selection and aggregate monotonicity are compatible with individual rationality, the dummy player property and symmetry for single-valued solutions defined on both G ^N and E ^N . This result solves an open question in the literature (see for example Young et?al. Water Resour Res 18:463?C475, 1982).     

Mössbauer and X-ray study of rapidly quenched and mechanically alloyed Al-Fe alloys

Mössbauer spectroscopy and X-ray diffractometry were used to study the effect of the cooling rate as well as of the milling time on the structure of rapidly quenched Al-6.8% Fe, Al-0.5% Fe and mechanically alloyed Al-8% Fe alloys. The main phase of the rapidly quenched alloys was identified as Al _m Fe besides Al₆Fe andAlFe solid solutions. In the mechanically alloyed samples (with milling time between 1.5–43 hours), we have found -Fe, AlFe solid solution and a third phase characterized by a doublet with Mössbauer parameters which are not so far from those of clusters inAlFe alloys. We have observed a continuous increase of the quantity ofAlFe solid solution, together with a significantly less increase of the third phase as a function of the milling time. Simultaneously, the quantity of alpha-iron has gradually decreased.     

Temperature dependence of positron annihilation parameters in tin

The positron mean life and the Doppler broadening of the annihilation line were measured in tin from ?196°C to 220°C. A small increase with temperature was observed in the values of these parameters.     

Connection problems in mountains and monotonic allocation schemes

Directed minimum cost spanning tree problems of a special kind are studied, namely those which show up in considering the problem of connecting units (houses) in mountains with a purifier. For such problems an easy method is described to obtain a minimum cost spanning tree. The related cost sharing problem is tackled by considering the corresponding cooperative cost game with the units as players and also the related connection games, for each unit one. The cores of the connection games have a simple structure and each core element can be extended to a population monotonic allocation scheme (pmas) and also to a bi-monotonic allocation scheme. These pmas-es for the connection games result in pmas-es for the cost game.     

A class of stochastic games with ordered field property

It is shown that discounted general-sum stochastic games with two players, two states, and one player controlling the rewards have the ordered field property. For the zero-sum case, this result implies that, when starting with rational data, also the value is rational and that the extreme optimal stationary strategies are composed of rational components.     

A note on the characterizations of the compromise value

In Borm, Keiding, McLean, Oortwijn and Tijs (1992) the compromise value is introduced as a solution concept on the class of compromise admissible NTU-games. Two characterizations of the compromise value are provided on subclasses of NTU-games. This note shows that in one of these characterizations the axioms are dependent. As a result of this observation a new characterization of the compromise value is provided. Moreover, it turns out that with a small weakening of the symmetry property the axioms in the original characterization become independent. Further, it is shown that these characterizations can be extended to a larger class of NTU-games. Finally, all monotonic, Pareto optimal, and covariant values on this class of NTU-games are described.     

On the existence of values for arbitration games

Two-person games in normal form are considered, where the players may use correlated strategies and where the problem arises, which Pareto optimal point in the payoff region to choose. We suppose that the players solve this problem with the aid of an arbitration function, which is continuous and profitable, and for which the inverse image of each Pareto point is a convex set. Then the existence of values and defensive ε-optimal strategies is discussed. Existence theorems are derived, using families of suitable dummy zero-sum games. The derived existence theorems contain all known existence results as special cases.     

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.     

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.