Kenjiro Nakamura

The vetoers in a simple game with ordinal preferences

We consider a core of a simple game with ordinal preferences on a set of alternative outcomes Ω. When a players strict preference relation takes any logically possible form of acyclic binary relation on Ω, necessary conditions for a simple game to have a nonempty core are given. If Ω is a finite set, the conditions are also sufficient. Further some related results are obtained.

Roles of Atomic Hydrogen in Chemical Annealing

A systematic study has been performed to reveal the role of atomic hydrogen in chemical annealing, where the deposition of a thin layer and treatment with atomic hydrogen are repeated alternately, for the fabrication of a stable structure. Structural relaxation resulting from impingement of atomic hydrogen on the growing surface is differentiated into two processes: the structural promoted relaxation on the surface and changes caused within the sub-surface depending on the conditions for deposition of the thin layer and the flux of atomic hydrogen. The structural changes within the sub-surface resulted in either the widening of the optical gap or crystallization at rather low substrate temperatures (T s: 100-150° C). High-quality a-Si:H with the optical gap of 1.87 eV exhibiting rather high stability against light soaking was successfully fabricated by this technique. The defect density of the film was 4×1015 cm-3 in its well annealed state and 6×1016 cm-3 in the saturated state. At high T s, on the other hand, the hydrogen treatment mainly enhanced chemical activities of the growing surface and resulted in either narrowing of the optical gap or promotion of the grain growth.

The Nash Social Welfare Function

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. The Econometric Society is collaborating with JSTOR to digitize, preserve and extend access to Econometrica. We investigate the notion o0f the Nash social welfare function and make a fundamental assumption that there exists a distinguished alternative called an origin, which represents one of the worst states for all individuals in the society. Under this assumption, in Sections 1 and 2, we formulate several rationality criteria that a reasonable social welfare function should satisfy. Then we introduce the Nash social welfare function and the Nash social welfare indices which are the images of the welfare function. The function is proved to satisfy the criteria. In Section 3 it is shown that the Nash social welfare function is the unique social welfare function that satisfies the criteria. Then, in Section 4, we examine two examples which display plausibility of the welfare function.

The core of a simple game with ordinal preferences

Michael Dummett andRobin Farquharson [1961] provided a sufficient condition for ann-person simple majority game with ordinal preferences to have a nonempty core. In the present paper we generalize this result to an arbitrary proper simple game. It is proved that their condition is also sufficient for this game to have a nonempty core. Our proof of this theorem is much simpler than the proof given byDummett andFarquharson. Finally some applications of the theorem are presented.

The strategy-proof social choice functions

The necessary conditions for a social choice function to be coalitionally strategy-proof are provided by using a main theorem of Nakamura (1975b) , when the set of individuals is any non-empty set. As a corollary of this result, we derived the Gibbard–Satterthwaite theorem [ Gibbard (1973) and Satterthwaite (1975) ].

Representation of characteristic function games by social choice functions

In Pelegs investigation of the representation of a simple game by a social choice function, it is shown that a special kind of proper symmetric simple game has its representation by employing the elimination procedure. In this paper, we consider a representation of a characteristic function game and explore general conditions under which the elimination procedure works effectively.

Fabrication of high quality silicon related films with band-gap of 1.5 eV by chemical annealing

Abstract Hydrogen radical flux tended to promote crystallization at substrate temperature higher than 200°C accompanying reduction in the hydrogen content. By the addition of Ar∗ into H, the crystallization was partly prevented with the aid of ion-bombardment. Addition of a small amount of Ge efficiently prevented the crystallization induced by chemical annealing at higher substrate temperature. Consequently, a-SiGe0.1:H with a band-gap of 1.67 eV with a defect density less than 6 × 1015 cm−3 was fabricated by chemical annealing at Ts = 250°C. a-SiGe0.2:H with a band-gap of ∼ 1.5 eV showing low defect density was successfully made by preventing permeation of hydrogen into Si-network with the aid of Ar∗.

On thek-stability ofm-quota games

We consider thek-stability ofm-quota games ofn players. We prove that anm-quota game (N, v), which satisfies the conditionv(S)=0 for allS, ¦S¦ ≤m −1, is (m −1)-stable if and only if there is no weak player. Further, some relationships between ak-stable pair and anm-quota are shown. Some ofLuces results [1955] on Shapley quota games are generalized tom-quota games.

Structural relaxation on growing surface during network formation of a-Si:H and a-SiGex:H by chemical annealing

Investigation was made into the role of long-lived species, i.e., atomic hydrogen and excited states of noble gases in “Chemical Annealing (CA)” in making hydrogenated amorphous silicon (a-Si:H) and a-SiGex:H. Distinctive differences were found between Si and Ge in their behaviour on the growing surface in CA-mode, as follows: (1) atomic hydrogen was mainly used to remove the hydrogen covering the growing surface of a-Si:H, but to passivate dangling bonds (DB) on the surface of a-Ge:H; and (2) ion bombardment with excited noble gases such as Ne + under application of DC bias (negative) caused the difference in hydrogen content (C H at%), tendencies to increase and decrease, respectively.

ψ-Stability of a cooperative game without side payments

In the present paper we defineψ-stability for theAumann-Peleg theory of cooperative games without side payments, and we prove some theorems which are analogous to the core theorem byAumann andBurger. These theorems provide foundations of the theory ofψ-stability for cooperative games without side payments in addition to being of interest for their own sake. We also consider the composition of two admissible functionsψ1 andψ2.