Price vs Quantity in Duopoly Supergames with Close Substitutes

We model the non-cooperative choice between quantity and price in order to stabilize collusion, through two meta-games where each firm alternatively considers its payoff in the market supergame as directly related to its own or the rival's ability to collude. In the first setting, (i) if cartel profits are evenly split, firms collude in prices irrespective of the degree of differentiation, so that initially a Prisoners' Dilemma is observed, while for very close substitutes the outcome is Pareto-efficient; (ii) if Nash bargaining is adopted, price setting is dominant when substitutability is low, while no dominant strategy exists when substitutability is high, and the game has two asymmetric equilibria. In the second setting, the Nash equilibrium is unique and Pareto-e±cient for the most part of the substitutability range, while again two asymmetric equilibria obtain when products are very close substitutes

Infall near clusters of galaxies: comparing gas and dark matter velocity profiles

We consider the dynamics in and near galaxy clusters. Gas, dark matter and galaxies are presently falling into the clusters between approximately 1 and 5 virial radii. At very large distances, beyond 10 virial radii, all matter is following the Hubble flow, and inside the virial radius the matter particles have on average zero radial velocity. The cosmological parameters are imprinted on the infall profile of the gas, however, no method exists, which allows a measurement of it. We consider the results of two cosmological simulations (using the numerical codes RAMSES and Gadget) and find that the gas and dark matter radial velocities are very similar. We derive the relevant dynamical equations, in particular the generalized hydrostatic equilibrium equation, including both the expansion of the Universe and the cosmological background. This generalized gas equation is the main new contribution of this paper. We combine these generalized equations with the results of the numerical simulations to estimate the contribution to the measured cluster masses from the radial velocity: inside the virial radius it is negligible, and inside two virial radii the effect is below 40%, in agreement the earlier analyses for DM. We point out how the infall velocity in principle may be observable, by measuring the gas properties to distance of about two virial radii, however, this is practically not possible today.Comment: 7 pages, 3 figures, to appear in MNRA

Dimensions of the Wage-Unemployment Relationship in the Nordic Countries: Wage Flexibility Without Wage Curves

No abstract.