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 probabilistic position value
In this article, we generalize the position value, defined by Meessen (Master’s thesis, 1988) for the class of deterministic communication situations, to the class of generalized probabilistic communication situations (Gómez et al. in European Journal of Operational Research 190:539–556, 2008). We provide two characterizations of this new allocation rule. Following in Slikker’s (International Journal of Game Theory 33:505–514, 2005a) footsteps, we characterize the probabilistic position value using probabilistic versions of component efficiency and balanced link contributions. Then we generalize the notion of link potential, defined by Slikker (International Game Theory Review 7:473–489, 2005b) for the class of deterministic communication situations, to the class of generalized probabilistic communication situations, and use it to characterize our allocation rule.
Communication Games
The communicative approach to language teaching proposes that games can create an ideal framework for meaningful interaction in the language classroom. Except for rare examples of empirical studies, for example, Gardner (1988), these assumptions rely mainly on theoretical justifications and on random observations by teachers. Because of the numerous variables involved in a language game activity, it is extremely difficult to gain pure empirical data and give a comprehensible analysis of all the factors. However, I feel that a closer observation of the factors that have been commented