The optimal prize structure of symmetric Tullock contests

We show that the optimal prize structure of symmetric n-player Tullock tournaments assigns the entire prize pool to the winner, provided that a symmetric pure strategy equilibrium exists. If such an equilibrium fails to exist under the winner-take-all structure, we construct the optimal prize structure which improves existence conditions by dampening efforts. If no such optimal equilibrium exists, no symmetric pure strategy equilibrium induces positive efforts

Equilibrium Structure of Production Economies with Uncertainty: The Natural Projection Approach

The paper generalizes the natural projection approach introduced by Balasko (1988) to production economies with uncertainty. It explores the equilibrium structure of the long run and short run private ownership production model. It is shown that qualitative equilibrium properties of the production model are those of the exchange model with production adjusted demand functions.Existence of Equilibrium, Equilibrium Structure, Uncertainty, Production.

Comment on "On the importance of the free energy for elasticity under pressure"

Marcus et al. (Marcus P, Ma H and Qiu S L 2002 J. Phys.: Condens. Matter 14 L525) claim that thermodynamic properties of materials under pressure must be computed using the Gibbs free energy $G$, rather than the internal energy $E$. Marcus et al. state that ``The minima of $G$, but not of $E$, give the equilibrium structure; the second derivatives of $G$, but not of $E$, with respect to strains at the equilibrium structure give the equilibrium elastic constants.'' Both statements are incorrect.Comment: Commen

The Equilibrium Structure of Prolate Magnetized Molecular Cores

The structure of molecular cloud cores supported by thermal pressure and a poloidal magnetic field is reinvestigated in the magnetohydrostatic and axisymmetric approximation. In addition to oblate configurations found in earlier work, solutions yielding prolate spheroidal shapes have also been obtained for a reference state described by a uniform sphere threaded by a uniform background magnetic field. The solutions for prolate configurations are found to be relevant for lower masses than for their oblate counterparts. Of particular importance is the result that the prolate cloud cores have radii less than a maximum given by $0.25 pc (a/0.2km/s)^2 (P_{\rm ext}/10^{-12} dyne/cm^2)^{-1/2}$, where $a$ is the sound speed and $P_{\rm ext}$ is the external pressure of the background medium. The existence of such solutions obviates the presence of toroidal fields in such modeled structures.Comment: 5 pages, 3 figures. Accepted for publication by ApJ