An Introduction to Fair and Non-Manipulable Allocations of Indivisible Objects

This paper analyzes a way of allocating primarily three indivisible objects to the same number of individuals. We define an allocation rule that, given the preferences of the individuals, distributes an amount of money together with exactly one indivisible object to each of the individuals in a fair and optimal way. The monetary distributions are foremost interpreted as compensations and are regulated by an exogenously given upper limit. We examine some of the rule's properties, with the most important one being that the rule is coalitionally strategy-proof

Complexity of finding Pareto-efficient allocations of highest welfare

We allocate objects to agents as exemplified primarily by school choice. Welfare judgments of the objectallocating agency are encoded as edge weights in the acceptability graph. The welfare of an allocation is the sum of its edge weights. We introduce the constrained welfare-maximizing solution, which is the allocation of highest welfare among the Pareto-efficient allocations. We identify conditions under which this solution is easily determined from a computational point of view. For the unrestricted case, we formulate an integer program and find this to be viable in practice as it quickly solves a real-world instance of kindergarten allocation and large-scale simulated instances. Incentives to report preferences truthfully are discussed briefly

Assignment Games with Externalities

We examine assignment games, wherematched pairs of firms and workers create some monetary value to distribute among themselves and the agents aim to maximize their payoff. In the majority of this literature, externalities - in the sense that a pair’s value depends on the pairing of the others - have been neglected. However, inmost applications a firm’s success depends on, say, the success of its rivals and suppliers. Thus, it is natural to ask how the classical results on assignment games are affected by the introduction of externalities? The answer is – dramatically. We find that (i) a problem may have no stable outcome, (ii) stable outcomes can be inefficient (not maximize total value), (iii) efficient outcomes can be unstable, and (iv) the set of stable outcomes may not form a lattice. We show that stable outcomes always exist if agents are "pessimistic." This is a knife-edge result: there are problems in which the slightest optimism by a single pair erases all stable outcomes

Assignment games with externalities revisited

We study assignment games with externalities. The value that a firm and a worker create depends on the matching of the other firms and workers. We ask how the classical results on assignment games are affected by the presence of externalities. The answer is that they change dramatically. Though stable outcomes exist if agents are “pessimistic”, this is a knife-edge result: we show that there are problems in which the slightest optimism by a single pair erases all stable outcomes. If agents are sufficiently optimistic, then there need not exist stable outcomes even if externalities are vanishingly small. The negative result persists also when we impose a very restrictive structure on the values and the externalities. Furthermore, stability and efficiency no longer go hand in hand and the set of stable outcomes need not form a lattice with respect to the agents’ payoffs

Multi-mode transport through a quantum nanowire with two embedded dots

We investigate the conductance of a quantum wire with two embedded quantum dots using a T-matrix approach based on the Lippmann-Schwinger formalism. The quantum dots are represented by a quantum well with Gaussian shape and the wire is two-dimensional with parabolic confinement in the transverse direction. In a broad wire the transport can assume a strong nonadiabatic character and the conductance manifests effects caused by intertwined inter- and intra-dot processes that are identified by analysis of the ``nearfield'' probability distribution of the transported electrons.Comment: RevTeX, 7 pages with included postscript figure

Transport through a quantum ring, a dot and a barrier embedded in a nanowire in magnetic field

We investigate the transport through a quantum ring, a dot and a barrier embedded in a nanowire in a homogeneous perpendicular magnetic field. To be able to treat scattering potentials of finite extent in magnetic field we use a mixed momentum-coordinate representation to obtain an integral equation for the multiband scattering matrix. For a large embedded quantum ring we are able to obtain Aharanov-Bohm type of oscillations with superimposed narrow resonances caused by interaction with quasi-bound states in the ring. We also employ scattering matrix approach to calculate the conductance through a semi-extended barrier or well in the wire. The numerical implementations we resort to in order to describe the cases of weak and intermediate magnetic field allow us to produce high resolution maps of the ``near field'' scattering wave functions, which are used to shed light on the underlying scattering processes.Comment: RevTeX, 13 pages with included postscript figures, high resolution version available at http://hartree.raunvis.hi.is/~vidar/Rann/VG_04.pd

Fracturing and vein formation in the middle crust - a record of co-seismic loading and post-seismic stress relaxation

Metamorphic rocks approaching the crustal scale brittle-ductile transition (BDT) during exhumation are expected to become increasingly affected by short term stress fluctuations related to seismic activity in the overlying seismogenic layer (schizosphere), while still residing in a long-term viscous environment (plastosphere). The structural and microstructural record of quartz veins in low grade – high pressure metamorphic rocks from southern Evia, Greece, yields insight into the processes and conditions just beneath the long-term BDT at temperatures of about 300 to 350°C, with switches between brittle failure and viscous flow as a function of imposed stress or strain rate...conferenc

Coherent electronic transport in a multimode quantum channel with Gaussian-type scatterers

Coherent electron transport through a quantum channel in the presence of a general extended scattering potential is investigated using a T-matrix Lippmann-Schwinger approach. The formalism is applied to a quantum wire with Gaussian type scattering potentials, which can be used to model a single impurity, a quantum dot or more complicated structures in the wire. The well known dips in the conductance in the presence of attractive impurities is reproduced. A resonant transmission peak in the conductance is seen as the energy of the incident electron coincides with an energy level in the quantum dot. The conductance through a quantum wire in the presence of an asymmetric potential are also shown. In the case of a narrow potential parallel to the wire we find that two dips appear in the same subband which we ascribe to two quasi bound states originating from the next evanescent mode.Comment: RevTeX with 14 postscript figures include