Proper Simple Game Research Articles

A bargaining set for monotonic simple games based on external and internal stability

A new bargaining set based on notions of both internal and external stability is developed in the context of endogenous coalition formation. It allows one to make an explicit distinction between within-group and outside-group deviation options. This type of distinction is not present in current bargaining sets. For the class of monotonic proper simple games, the outcomes in the bargaining set are characterized. Furthermore, it is shown that the bargaining set of any homogeneous weighted majority game contains an outcome for which the underlying coalition structure consists of a minimal winning coalition and its complement.

Coalitional stability with a credibility constraint

Following Chwe (1994) we introduce a similar notion of coalitional stability for proper simple games with the additional desirable property that a coalition moves to an outcome stable with respect to this notion only when the outcome is not dominated by another stable outcome. We call a set of outcomes stable with respect to this notion a credibly consistent set. We examine the issue of the existence and non-emptiness of such sets and investigate their relation to some other solution concepts prevalent in the literature concerning coalitional stability.

The desirability relation of simple games

We prove some properties of simple games with a complete desirability relation, and investigate the relationships between the desirability of a simple game G and that of some simple games that are derived from G. We also provide an example of a proper simple game that has a complete and acyclic desirability relation but is not a weighted majority game.

Heights of simple games

We consider simple games which are constructed as iterated weighted majority games. It turns out that every proper simple game can be obtained in this way. The minimal number of iterations necessary to obtain a given game is called the height of this game. We investigate the behaviour ofh (n), the maximal height of a simple game withn players.

序数的選好関係をもつ投票ゲームの安定集合について

In this paper, stable sets for simple games with ordinal preferences are studied in the case where the number of alternatives is finite. It is shown that the condition for the existence of a nonempty core for any possible combination of players' preferences is also a necessary and sufficient condition for the existence of a unique stable set. Moreover, a necessary and sufficient condition that proper simple games have at least one stable set is presented.

A further result on the core of voting games

LetN be a set of individuals,A a closed bounded interval ofRe. Using a former result ofNakamura, it is shown that if every individual inN has a quasi-concave utility function overA, then a proper simple game has a non-empty core which is a convex set. In particular, the majority core is explicitly characterized. When every individual inN has a strictly quasi-concave utility function overA, then it is shown that the local core in a proper simple game is precisely the core.

Necessary and sufficient conditions for transitivity in voting theory

In this paper we provide necessary and sufficient conditions for transitivity of the social preferences given by two types of social decision processes. We consider transitivity of the dominance relation of a proper simple game and that of the social preference given by the simple majority decision rule.

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.