The Banzhaf index and the Shapley-Shubik index are the best-known and the most used tools to measure political power of voters in a voting system. Most methods to calculate these power indices are based on counting winning coalitions, in particular those coalitions a voter is decisive for. We present a new combinatorial formula to calculate both indices solely using the set of minimal winning c...

Rationalizability and similar notions of consistency have proved to be highly problematic in the context of social choice, as witnessed by a range of impossibility results, among which Arrow’s is the most prominent. We propose to rationalize choice functions by preference relations over sets of alternatives (set-rationalizability) and introduce two consistency conditions, α̂ and γ̂, which are def...

IUR cooperation is the cooperation of different profit subjects. Much IUR cooperation is not successful, although it can bring about excess earnings and has endured tremendous development. The crux conflict lies in the unreasonable profits allocation way. Fair and reasonable profits allocation playing the important role of motive mechanism which facilitates cooperation of partners. This essay a...

We introduce stochastic priority games — a new class of perfect information stochastic games. These games can take two different, but equivalent, forms. In stopping priority games a play can be stopped by the environment after a finite number of stages, however, infinite plays are also possible. In discounted priority games only infinite plays are possible and the payoff is a linear combination...

Oxygen utilization is defined in this investigation as the terminal use of oxygen in respiration, i.e., the formation of water. A culture of Pseudomonas fluorescens was allowed to respire in an atmosphere of O(18). The production of H(2)O(18) was measured during two test runs of 124 and 232 min each. During the first run, 0.505 mmole of H(2)O(18) was produced. The second run produced 0.460 mmol...

In this paper we propose a context-specific cost allocation rule for inventory transportation systems. We consider the setting defined in Fiestras-Janeiro et al. (2012) [3] and propose a new cost allocation rule, the so-called AMEF value, which is inspired by the Shapley value. We prove that, under suitable conditions, the AMEF value provides core allocations. Besides, we provide a characteriza...

One of the main issues in economics is the trade-off between marginalism and egalitarianism. In the context of cooperative games this trade-off can be framed as one of choosing to allocate according to the Shapley value or the equal division solution. In this paper we provide tools that make it possible to study this trade-off in a consistent way by providing three types of results on egalitari...

We incorporate externalities into the stable matching theory of two-sided markets: We establish the existence of stable matchings provided that externalities are positive and agents’ choices satisfy substitutability, and we show that the standard insights of matching theory, such as the existence of side optimal stable matchings and the rural hospitals theorem, remain valid despite the presence...

We consider mixed cost allocation problems, i.e., joint cost problems in which there are two types of heterogeneous outputs : Divis-ible and indivisible ones. The Aumann-Shapley price mechanism is extended to this setting. We also present a set of properties which characterize this cost sharing rule.

The Penrose-Banzhaf index and the Shapley-Shubik index are the best-known and the most used tools to measure political power of voters in simple voting games. Most methods to calculate these power indices are based on counting winning coalitions, in particular those coalitions a voter is decisive for. We present a new combinatorial formula how to calculate both indices solely using the set of m...