A decision support method for designing vegetation layers with minimised irrigation need

Annals of Operations Research - Selecting a vegetation layer design goes along with determining its future irrigation need. Therefore, it is essential to take a design decision that is minimising...     

Spanning network games

We study fundamental properties of monotone network enterprises which contain public vertices and have positive and negative costs on edges and vertices. Among the properties studied are the nonemptiness of the core, characterization of nonredundant core constraints, ease of computation of the core and the nucleolus, and cases of decomposition of the core and the nucleolus. Received December 1994/Final version March 1998     

Asymptotic stability and other properties of trajectories and transfer sequences leading to the bargaining sets

The foundation of a dynamic theory for the bargaining sets started withStearns, when he constructed transfer sequences which always converge to appropriate bargaining sets. A continuous analogue was developed byBillera, where sequences where replaced by solutions of systems of differential equations. In this paper we show that the nucleolus is locally asymptotically stable both with respect toStearns' sequences andBillera's solutions if and only if it is an isolated point of the appropriate bargaining set. No other point of the bargaining set can be locally asymptotically stable. Furthermore, it is always stable in these processes. As by-products of the study we derive the results ofBillera andStearns in a different fashion. We also show that along the non-trivial trajectories and sequences, the vector of the excesses of the payoffs, arranged in a non-increasing order, always decreases lexicographically, thus each bargaining set can be viewed as resulting from a certain monotone process operating on the payoff vectors.     

Entanglement assisted fast reordering of atoms in an optical lattice within a cavity at T = 0

Laser-illuminated atoms in an optical resonator exhibit a phase transition between the homogenous distribution and two possible ordered configurations in the optical lattice formed by the cavity and pump fields. At zero temperature, atom-field entanglement plays a crucial role in the spatial reordering of the atoms from a homogeneous towards the two ordered states, where all atoms occupy either only even or only odd lattice sites. Concurrent with the buildup of atom-field entanglement, the homogeneous atomic cloud evolves immediately into the superposition of the two stable patterns entangled with opposite cavity field amplitudes. This possibility is absent in a factorized (classical) treatment of atoms and field and should be generic for spontaneous symmetry breaking in quantum phase transitions in optical potentials.     

The general nucleolus and the reduced game property

The nucleolus of a TU game is a solution concept whose main attraction is that it always resides in any nonempty -core. In this paper we generalize the nucleolus to an arbitrary pair (,F), where is a topological space andF is a finite set of real continuous functions whose domain is . For such pairs we also introduce the least core concept. We then characterize the nucleolus forclasses of such pairs by means of a set of axioms, one of which requires that it resides in the least core. It turns out that different classes require different axiomatic characterizations.One of the classes consists of TU-games in which several coalitions may be nonpermissible and, moreover, the space of imputations is required to be a certain generalized core. We call these gamestruncated games. For the class of truncated games, one of the axioms is a new kind ofreduced game property, in which consistency is achieved even if some coalitions leave the game, being promised the nucleolus payoffs. Finally, we extend Kohlberg's characterization of the nucleolus to the class of truncated games.     

The kernel and bargaining set for convex games

It is shown that for convex games the bargaining set? ₁ ⁽ⁱ⁾ (for the grand coalition) coincides with the core. Moreover, it is proved that the kernel (for the grand coalition) of convex games consists of a unique point which coincides with the nucleolus of the game.     

A demand adjustment process

The aspiration approach to cooperative games, which has been studied by a number of authors, including Cross, Turbay, Albers, Selten and Bennett, presumes that players in a game bargain over their reservation prices, or aspirations. A number of aspiration-based solution concepts have been put forth, and aspiration solutions have been connected to non-cooperative bargaining models. Missing in this approach has been theory of how aspirations themselves arise. The present paper is an attempt to fill this gap. It describes a very general demand adjustment process, using the framework of set-valued dynamical systems developed by Maschler and Peleg. This demand adjustment process always converges; sufficient conditions are given in order that it converge to an aspiration, and that it converge in a finite number of steps.     

Central Kähler metrics with non-constant central curvature

The central curvature of a Riemannian metric is the determinant of its Ricci endomorphism, while the scalar curvature is its trace. A Kähler metric is called central if the gradient of its central curvature is a holomorphic vector field. Such metrics may be viewed as analogs of the extremal Kähler metrics defined by Calabi. In this work, central metrics of non-constant central curvature are constructed on various ruled surfaces, most notably the first Hirzebruch surface. This is achieved via the momentum construction of Hwang and Singer, a variant of an ansatz employed by Calabi (1979) and by Koiso and Sakane (1986). Non-existence, real-analyticity and positivity properties of central metrics arising in this ansatz are also established.     

Conformally Kähler base metrics for Einstein warped products

A Riemannian metric g with Ricci curvature r is called nontrivial quasi-Einstein, in a sense given by Case, Shu and Wei, if it satisfies (−a/f)∇df+r=λg, for a smooth nonconstant function f and constants λ and a>0. If a is a positive integer, it was noted by Besse that such a metric appears as the base metric for certain warped Einstein metrics. This equation also appears in the study of smooth metric measure spaces. We provide a local classification and an explicit construction of Kähler metrics conformal to nontrivial quasi-Einstein metrics, subject to the following conditions: local Kähler irreducibility, the conformal factor giving rise to a Killing potential, and the quasi-Einstein function f being a function of the Killing potential. Additionally, the classification holds in real dimension at least six. The metric, along with the Killing potential, form an SKR pair, a notion defined by Derdzinski and Maschler. It implies that the manifold is biholomorphic to an open set in the total space of a CP¹ bundle whose base manifold admits a Kähler-Einstein metric. If the manifold is additionally compact, it is a total space of such a bundle or complex projective space. Additionally, a result of Case, Shu and Wei on the Kähler reducibility of nontrivial Kähler quasi-Einstein metrics is reproduced in dimension at least six in a more explicit form.     

The super-additive solution for the Nash bargaining game

The feasible set in a Nash bargaining game is a set in the utility space of the players. As such, its points often represent expectations on uncertain events. If this is the case, the feasible set changes in time as uncertainties resolve. Thus, if time for reaching agreement is not fixed in advance, one has to take into account options for delaying an agreement. This paper studies such games and develops a solution concept which has the property that its followers will always prefer to reach an immediate agreement, rather than wait until a new feasible set arises.