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.
A Value for Directed Communication Situations
In this paper we introduce an extension of the model of restricted communication in cooperative games as introduced in Myerson (1977) by allowing communication links to be directed and the worth of a coalition to depend on the order in which the players enter the coalition. Therefore, we model the communication network by a directed graph and the cooperative game by a generalized characteristic function as introduced in Nowak and Radzik (1994). We generalize the Myerson value for undirected (or standard) communication situations to the context of directed communication and provide two axiomatizations of this digraph Myerson value using component efficiency and either fairness or the balanced contributions property.
A Value with Incomplete Communication
The aim of this paper is to present a new value of a cooperative game for the case of limited communication between players. The communication system we consider may be represented by a simple graph, that is, only pairwise meetings can occur and some of them are not permitted. An associated game is defined and the value has to verify a consistency axiom.