On the equivalence of G-weak and -strong cores in the marriage problem

In the marriage problem (two-sided one-to-one matching problem), it is well-known that the weak core, the strong core and the set of stable matchings are all equivalent. This paper generalizes the above observation considering the G-weak core and the G-strong core. These are core concepts in which blocking power is restricted to the coalitions belonging to the prescribed class of coalitions G. I give a necessary and sufficient condition that G should satisfy for the equivalence of the G-weak core and the G-strong core.

On the Equivalence of G-weak and -strong Cores in the Marriage Problem

In the marriage problem (two-sided one-to-one matching problem), it is well-known that the weak core, the strong core and the set of stable matchings are all equivalent. This paper generalizes the above observation considering the G-weak core and the G-strong core. These are core concepts in which blocking power is restricted to the coalitions belonging to the prescribed class of coalitions G. I give a necessary and sufficient condition that G should satisfy for the equivalence of the G-weak core and the G-strong core.

Mutual Knowledge of Rationality in the Electronic Mail Game

This paper reexamines the paradoxical aspect of the electronic mail game (Rubinstein, 1989). The electronic mail game is a coordination game with payoff uncertainty. At a Bayesian Nash equilibrium of the game, players cannot achieve the desired coordination of actions even when a high order of mutual knowledge of payoff functions obtains. We want to make explicit the role of knowledge about rationality of players, not only that of payoff functions. For this purpose, we use an extended version of the belief system model developed by Aumann and Brandenburger (1995). We propose a certain way of embedding the electronic mail game in an belief system. And we show that for rational players to coordinate their actions, for any embedding belief systems, it is necessary that the upper bound order of mutual knowledge of payoff functions exceeds the upper bound order of mutual knowledge of rationality. This result implies that under common knowledge of rationality, the coordination never occurs, which is similar to Rubinstein's result. We point out, however, that there exists a class embedding belief systems for which the above condition is also sufficient for the desired coordination.

Computational Complexity in the Design of Voting Rules

This paper discusses an aspect of computational complexity in social choice theory. We consider the problem of designing voting rules, which is formulated in terms of simple games. We prove that it is an NP-complete problem to decide whether a given simple game is stable, or not.

A case of type 1 facioscapulohumeral muscular dystrophy (FSHD) with restrictive ventilatory defect and congestive heart failure

[Background] Facioscapulohumeral muscular dystrophy (FSHD) is an autosomal dominant muscle disease characterized by asymmetric involvement of muscles in the face, upper extremity, trunk, and lower extremity regions, with variable severity. It was recently reported that restrictive respiratory involvement is more frequent and severe than previously recognized, while cardiac dysfunction other than arrhythmia is still considered extremely rare in FSHD. [Case report] A 59-year-old man presenting with marked muscle atrophy in the trunk and asymmetrical muscle atrophy in the legs was hospitalized because of dyspnea and edema in the face and limbs. Shortness of breath with body movement started from approximately 40 years of age. Muscle biopsy revealed myopathic change with mild to moderate variation in fiber size. The diagnosis of FSHD was made by D4Z4 contraction to three repeats on genetic testing. A pulmonary function test revealed a decline of forced vital capacity (FVC) and a preserved FEV1/FVC indicating restrictive ventilatory defect (RVD). Ultrasonic echocardiogram (UCG) showed diffuse left ventricular hypokinesis, ventricular septum thickening, pericardial effusion, and decreased ejection fraction (LVEF 30%). [Conclusion] Although restrictive ventilatory defect and congestive heart failure are uncommon in FSHD, respiratory and cardiac evaluation may be necessary in patients with FSHD