Partial Strategyproofness: Relaxing Strategyproofness for the Random Assignment Problem

We present partial strategyproofness, a new, relaxed notion of strategyproofness for studying the incentive properties of non-strategyproof assignment mechanisms. Informally, a mechanism is partially strategyproof if it makes truthful reporting a dominant strategy for those agents whose preference intensities differ sufficiently between any two objects. We demonstrate that partial strategyproofness is axiomatically motivated and yields a parametric measure for "how strategyproof" an assignment mechanism is. We apply this new concept to derive novel insights about the incentive properties of the probabilistic serial mechanism and different variants of the Boston mechanism.Comment: Working Pape

Cosmological Perturbations in a Universe with a Domain Wall Era

Topologically protected sheet-like surfaces, called domain walls, form when the potential of a field has a discrete symmetry that is spontaneously broken. Since this condition is commonplace in field theory, it is plausible that many of these walls were produced at some point in the early universe. Moreover, for potentials with a rich enough structure, the walls can join and form a (at large scales) homogeneous and isotropic network that dominates the energy density of the universe for some time before decaying. In this thesis, we study the faith of large scale perturbations in a cosmology with a short period of domain wall dominance. Treating the domain wall network as a relativistic elastic solid at large scales, we show that the perturbations that exited the horizon during inflation get suppressed during the domain wall era, before re-entering the horizon. This power suppression occurs because, unlike a fluid-like universe, a solid-like universe can support sizable anisotropic stress gradients across large scales which effectively act as mass for the scalar and tensor modes. Interestingly, the amplitude of the primordial scalar power spectrum can be closer to one in this cosmology and still give the observed value of $10^{-9}$ today. As a result, the usual bounds on the energy scale of inflation get relaxed to values closer to the (more natural) Planck scale. In the last part of this thesis, as an existence proof, we present a hybrid inflation model with $N$ `waterfall' fields that can realize the proposed cosmology. In this model, a domain wall network forms when an approximate $O(N)$ symmetry gets spontaneously broken at the end of inflation, and for $N \geq 5$, we show that there is a region in parameter space where the network dominates the energy density for a few e-folds before decaying and reheating the universe.Comment: Ph.D. Thesis, Dec 201

On Iterated Dominance, Matrix Elimination, and Matched Paths

We study computational problems arising from the iterated removal of weakly dominated actions in anonymous games. Our main result shows that it is NP-complete to decide whether an anonymous game with three actions can be solved via iterated weak dominance. The two-action case can be reformulated as a natural elimination problem on a matrix, the complexity of which turns out to be surprisingly difficult to characterize and ultimately remains open. We however establish connections to a matching problem along paths in a directed graph, which is computationally hard in general but can also be used to identify tractable cases of matrix elimination. We finally identify different classes of anonymous games where iterated dominance is in P and NP-complete, respectively.Comment: 12 pages, 3 figures, 27th International Symposium on Theoretical Aspects of Computer Science (STACS

A note on blockers in posets

The blocker $A^{*}$ of an antichain $A$ in a finite poset $P$ is the set of elements minimal with the property of having with each member of $A$ a common predecessor. The following is done: 1. The posets $P$ for which $A^{**}=A$ for all antichains are characterized. 2. The blocker $A^*$ of a symmetric antichain in the partition lattice is characterized. 3. Connections with the question of finding minimal size blocking sets for certain set families are discussed

Melnikov's approximation dominance. Some examples

We continue a previous paper to show that Mel'nikov's first order formula for part of the separatrix splitting of a pendulum under fast quasi periodic forcing holds, in special examples, as an asymptotic formula in the forcing rapidity.Comment: 46 Kb; 9 pages, plain Te

A consistency check for Renormalons in Lattice Gauge Theory: beta^(-10) contributions to the SU(3) plaquette

We compute the perturbative expansion of the Lattice SU(3) plaquette to beta^(-10) order. The result is found to be consistent both with the expected renormalon behaviour and with finite size effects on top of that.Comment: 15 pages, 5 colour eps figures. Axes labels added in the figures. A comment added in the appendi

Map Matching with Simplicity Constraints

We study a map matching problem, the task of finding in an embedded graph a path that has low distance to a given curve in R^2. The Fr\'echet distance is a common measure for this problem. Efficient methods exist to compute the best path according to this measure. However, these methods cannot guarantee that the result is simple (i.e. it does not intersect itself) even if the given curve is simple. In this paper, we prove that it is in fact NP-complete to determine the existence a simple cycle in a planar straight-line embedding of a graph that has at most a given Fr\'echet distance to a given simple closed curve. We also consider the implications of our proof on some variants of the problem