A note on the ordinal equivalence of power indices in games with coalition structure
نویسندگان
چکیده
The desirability relation was introduced by Isbell (1958) to qualitatively compare the a priori influence of voters in a simple game. In this paper, we extend this desirability relation to simple games with coalition structure. In these games, players organize themselves into a priori disjoint coalitions. It appears that the desirability relation defined in this paper is a complete preorder in the class of swap-robust games. We also compare our desirability relation with the preorders induced by the generalizations to games with coalition structure of the Shapley-Shubik and Banzahf-Coleman power indices (Owen, 1977, 1981). It happens that in general they are different even if one considers the subclass of weighed voting games. However, if structural coalitions have equal size then both Owen-Banzhaf and the desirability preordering coincide.
منابع مشابه
Dichotomous multi-type games with a coalition structure
This work focuses on the evaluation of the voting power in dichotomous multi-type games endowed with a coalition structure (DMGCs). Dichotomous multi-type games have been introduced by Courtin et al. [2015] in order to generalize simple game. They modelize game in which there are a number of non-ordered types of support in the input, while the output is dichotomous, i.e. the proposal is accepte...
متن کاملMeasuring influence in command games
In the paper, we study a relation between command games proposed by Hu and Shapley and an influence model. We show that our framework of influence is more general than the framework of the command games. We define several influence functions which capture the command structure. These functions are compatible with the command games, in the sense that each commandable player for a coalition in th...
متن کاملA modified position value for communication situations and its fuzzification
Myerson treated various situations of cooperation in the field of cooperative games and proposed the communication structure. In this paper, we define and characterize an allocation rule in terms of the position value, called an average spanning tree solution, for communication situations by introducing a concept of cooperation relationship which says that two players are deemed to possess this...
متن کاملCoalition formation in general apex games under monotonic power indices
We generalize the class of apex game by combining a winning coalition of symmetric minor players with a collection of apex sets which can form winning coalitions only together with a fixed quota of minor players. By applying power indices to these games and their subgames we generate players’ preferences over coalitions which we use to define a coalition formation game. We focus on strongly mon...
متن کاملCombinatorial and computational aspects of multiple weighted voting games
Weighted voting games are ubiquitous mathematical models which are used in economics, political science, neuroscience, threshold logic, reliability theory and distributed systems. They model situations where agents with variable voting weight vote in favour of or against a decision. A coalition of agents is winning if and only if the sum of weights of the coalition exceeds or equals a specified...
متن کامل