Gluon Distribution Functions for Very Large Nuclei at Small Transverse Momentum

We show that the gluon distribution function for very large nuclei may be computed for small transverse momentum as correlation functions of an ultraviolet finite two dimensional Euclidean field theory. This computation is valid to all orders in the density of partons per unit area, but to lowest order in $\alpha_s$. The gluon distribution function is proportional to $1/x$, and the effect of the finite density of partons is to modify the dependence on transverse momentum for small transverse momentum.Comment: TPI--MINN--93--52/T, NUC--MINN--93--28/T, UMN--TH--1224/93, LaTex, 11 page

Hot Spots and Turbulent Initial Conditions of Quark-Gluon Plasmas in Nuclear Collisions

As a result of multiple mini-jet production, initial conditions of the QCD plasma formed in ultrarelativistic nuclear collisions may be inhomogeneous, with large fluctuations of the local energy density (hot spots), and turbulent, with a chaotic initial transverse velocity field. Assuming rapid local thermalization, the evolution of such plasmas is computed using longitudinal boost-invariant 3+1-dimensional hydrodynamics. We compare the evolution in case that the speed of sound in the plasma is constant to one resulting from an equation of state involving a strong first order transition, with a minimum of the velocity of sound as a function of energy density. We find that azimuthally asymmetric fluctuations and correlations of the transverse energy flow can develop in both cases due to the initial inhomogeneities. Hot spots also enhance significantly high-transverse momenta direct photon yields. In the case with a phase transition, the hadronization surface evolves into an unusual foam-like structure. Also in that case, we find that hadronization is considerably delayed relative to the ideal gas case, just as previous studies have found for homogeneous initial conditions. The time-delay signature of a rapid cross-over transition region in the QCD equation of state (as observable via meson interferometry) is thus found to be remarkably robust to uncertainties in the initial conditions in heavy-ion reactions.Comment: 28 pages, LaTeX, 20 figures, available as uucompressed file (including LaTeX-file) ftp://nt1.phys.columbia.edu/pub/turb/turb2.uu (username: ftp, password: complete email address

On the attainment of the maximum sustainable yield in the Verhulst-Lotka-Volterra model

We reformulate the Verhulst-Lotka-Volterra model of natural resource extraction under the alternative assumptions of Cournot behaviour and perfect competition, to revisit the tragedy of commons vs the possibility of sustainable harvesting. We stress the different impact of demand elasticity on the regulator’s possibility of driving industry harvest to the maximum sustainable yield in the two settings. The presence of a flat demand function offers the authority a fully effective regulatory tool in the form of the exogeneous price faced by perfectly competitive firms, to drive their collective harvest rate at the maximum sustainable yield. The same cannot happen under Cournot competition, as in this case the price is endogenous and the regulator’s policy is confined to limiting access to the common pool

Recent Studies on Incentive Design Problems in Game Theory and Management Science

We study a simple principal-agent game and show how the linear wage contract can be obtained by a three-phase adjustment process. The first two processes result in an incentive compatible Pareto optimal outcome and the third process takes care of the agent's individual rationality. We also discuss a negotiation process to achieve this outcome and give the wage contract an interpretation in terms of incentive equilibrium. This concept has recently been an active research topic in dynamic games and management science studies. In this paper we present a new method for computing incentive Stackelberg solutions. The method is based on solving a system of nonlinear equations by using standard iterative schemes such as fixedpoint iteration or Broyden's method. The method can be implemented in the case of incomplete information because the leader does not need to know the followers' reaction function. The use of the method is shown in two examples: in a two player quadratic case and in a duopoly model with government coordination. More general problems and convergence properties of the method are discussed