A New Outside Option Value for Networks: The Kappa-Value – Measuring Distribution of Power of Political Agreements
In an economic or social situation where agents have to group in order to achieve common goals, how can we calculate the coalitional rents of the agents arising from the coalition formation? Once we have formalized the situation via a TU-game and a network describing the economic structure, we can apply different allocation rules to assign the coalitional rents to the agents. We specifically analyze situations where parties with a specific vote distribution in a parliament have to build agreements in order to reach some required quorum. In this situation, we want to measure the (relative) distribution of power. We analyze the allocation rules called Position value (Meessen (1988) and Borm et al. (1992)) and graph-chi-value (Casajus (2009)). Applying the generalized framework (Gomez et al. (2008)), a framework where coalitions are not established yet, we fi nd that the graph-chi-value does not differ for networks referring to the same coalition while the Position value takes into account the specific role of an agent within the network, i.e. the communication path. We define and characterize a new outside option sensitive value, the Kappa-value, which takes into account both outside options and the role of an agent within the network.
The Shapley Value for n-Person Games in Generalized Characteristic Function Form
Abstract This paper is a first study of n -person games in coalitional form in which the characteristic functions are defined on all possible orders in coalitions of players. Such an approach seems to be useful in modeling some economic situations as well as some subtle relations between players in coalitions. Our main objective in this paper is to introduce axiomatically a unique value on the more general class of games indicated above. For the classical cooperative TU games our value coincides with the well-known Shapley value. We also discuss probabilistic values on the space of generalized games.
The General Theory of Relativity
THE WORD “SPECIAL” IN “SPECIAL THEORY OF RELATIVITY” means that the theory is restricted to those frames of reference for which the law of inertia holds, that is, inertial frames of reference.* Einstein sometimes referred to them as Galilean frames of reference. At first glance, it does not seem reasonable to expect that the principle of relativity can be extended to non-inertial frames. The reasons are fairly obvious. The principle of relativity that we have been using states that the laws of physics have the same form in all frames of reference to which the principle applies. In other words there should be no way to determine by an experiment which of two frames of reference is in motion relative to the other.