A note on the multiple partners assignment game

In the assignment game of Shapley and Shubik [Shapley, L.S., Shubik, M., 1972. The assignment game. I. The core, International journal of Game Theory 1, 11-130] agents are allowed to form one partnership at most. That paper proves that, in the context of firms and workers, given two stable payoffs for the firms there is a stable payoff which gives each firm the larger of the two amounts and also one which gives each of them the smaller amount. Analogous result applies to the workers. Sotomayor [Sotomayor, M., 1992. The multiple partners game. In: Majumdar, M. (Ed.), Dynamics and Equilibrium: Essays in Honor to D. Gale. Mcmillian, pp. 322-336] extends this analysis to the case where both types of agents may form more than one partnership and an agent`s payoff is multi-dimensional. Instead, this note concentrates in the total payoff of the agents. It is then proved the rather unexpected result that again the maximum of any pair of stable payoffs for the firms is stable but the minimum need not be, even if we restrict the multiplicity of partnerships to one of the sides. (C) 2009 Elsevier B.V. All rights reserved.

Adjusting prices in the multiple-partners assignment game

Starting with an initial price vector, prices are adjusted in order to eliminate the excess demand and at the same time to keep the transfers to the sellers as low as possible. In each step of the auction, to which set of sellers should those transfers be made is the key issue in the description of the algorithm. We assume additively separable utilities and introduce a novel distinction by considering multiple sellers owing multiple identical objects and multiple buyers with an exogenously defined quota, consuming more than one object but at most one unit of a seller`s good and having multi-dimensional payoffs. This distinction induces a necessarily more complicated construction of the over-demanded sets than the constructions of these sets for the other assignment games. For this approach, our mechanism yields the buyer-optimal competitive equilibrium payoff, which equals the buyer-optimal stable payoff. The symmetry of the model allows to getting the seller-optimal stable payoff and the seller-optimal competitive equilibrium payoff can then be also derived.

Vitamin D-Resistant Rickets Type II-A, Basal Ganglia Calcification, and Catatonia: A Casual or Causal Relationship?

Background: Vitamin D-resistant rickets type-IIA (VDRR-IIA) is a rare, congenital, metabolic disorder characterized by hypocalcemia, rickets, and alopecia. There are reports correlating calcium-metabolic disorders with basal ganglia calcification (BGC) and neuropsychiatric symptoms. Objective: The authors document and discuss the relationships of these phenomena. Method: The authors describe a patient born with VDRR-IIA who subsequently developed BGC at age 15, and catatonic symptoms of progressive severity at age 16. Results: There appeared to be a positive correlation between the severity of BGC and neuropsychiatric symptoms. Discussion: This is the first time VDRR-IIA, BGC, and catatonia have been reported in a patient, and the authors discuss the relationship among the conditions. (Psychosomatics 2009; 50: 420-424)

The game of leapfrog and the Internet: Developing countries and the information-divide

Recent rapid advances in communication technology have changed global structural patterns and produced new concepts and poles of dynamism in international relations. One such technology, which is increasingly causing a mixed reaction across international boundaries, is that of the Internet. For the first time in history the emergence of the Internet has produced an anarchic power that is capable of influencing individuals, societies and governments on a scale previously unimaginable.