Decreasing Serial Cost Sharing under Economies to Scale

We consider the problem of cost sharing in the presence of increasing returns to scale and potential strategic behavior on the part of consumers. We show that any smooth and strictly monotonic mechanism for which a Nash equilibrium exists for all profiles of convex and monotonic preferences must be dictatorial. However, we propose a cost sharing mechanism, the decreasing serial mechanism, for which an interesting domain restriction ensures existence of a noncooperative equilibrium for its cost sharing game. A characterization theorem of the mechanism based on the strategic properties of existence, uniqueness, and efficiency of its noncooperative equilibrium is provided.Publicad

Coalitional manipulations in a bankruptcy problem

In a bankruptcy problem framework we consider rules immune to possible manipulations by the creditors involved in the problem via merging or splitting of their individual claims. The paper provides characterization theorems for the non manipulable rules, the no advantageous merging parametric rules and the no advantageous splitting parametric rules.Publicad

On the Post-linear Quadrupole-Quadrupole Metric

The Hartle-Thorne metric defines a reliable spacetime for most astrophysical purposes, for instance for the simulation of slowly rotating stars. Solving the Einstein field equations, we added terms of second order in the quadrupole moment to its post-linear version in order to compare it with solutions found by Blanchet in the frame of the multi-polar post-Minkowskian framework. We first derived the extended Hartle-Thorne metric in harmonic coordinates and then showed agreement with the corresponding post-linear metric from Blanchet. We also found a coordinate transformation from the post-linear Erez-Rosen metric to our extended Hartle-Thorne spacetime. It is well known that the Hartle-Thorne solution can be smoothly matched with an interior perfect fluid solution with physically appropriate properties. A comparison among these solutions provides a validation of them. It is clear that in order to represent realistic solutions of self-gravitating (axially symmetric) matter distributions of perfect fluid, the quadrupole moment has to be included as a physical parameter

Optimal error bounds for two-grid schemes applied to the Navier-Stokes equations

We consider two-grid mixed-finite element schemes for the spatial discretization of the incompressible Navier-Stokes equations. A standard mixed-finite element method is applied over the coarse grid to approximate the nonlinear Navier-Stokes equations while a linear evolutionary problem is solved over the fine grid. The previously computed Galerkin approximation to the velocity is used to linearize the convective term. For the analysis we take into account the lack of regularity of the solutions of the Navier-Stokes equations at the initial time in the absence of nonlocal compatibility conditions of the data. Optimal error bounds are obtained

Trade disclosure and price dispersion

This paper determines the effects of post-trade opaqueness on market performance. We find that the degree of market transparency has important effects on market equilibria. In particular, we show that dealers operating in a transparent structure set regret-free prices at each period making zero expected profits in each of the two trading rounds, whereas in the opaque market dealers invest in acquiring information at the beginning of the trading day. Moreover, we obtain that if there is no trading activity in the first period, then market makers only change their quotes in the opaque market. Additionally, we show that trade disclosure increases the informational efficiency of transaction prices and reduces volatility. Finally, concerning welfare of market participants, we obtain ambiguous results