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 class of ASN-position values
This paper introduces a class of cooperative allocation rules for TU-games with a network structure that account for an agent’s centrality in the network. In contrast to existing centrality measures, this approach analyzes the consequences of tie failure (rather than node failure). Though not directly applied to the centrality issue, tie failures are the idea underlying the Position value (the Shapley value of the arc-game). In contrast, we allow for a whole class of allocation rules as a basis since the Shapley approach might be unreasonable in political applications, especially in networks with incompatibilities. Requiring additivity (A), equal treatment of equals (Symmetry S), and irrelevance of unproductive agents (nullplayer irrelevance N) for the underlying basis, we define the class of ASN-position values and provide axiomatic characterizations. To emphasize the crucial role of links, we refine this class to multiplicative ASN-position values and provide a monotonicity result with respect to links. We apply our approach to the case of the 2001 state parliament elections in Hamburg, Germany to use our allocation rule as a power index and further provide an example where we use our approach as a centrality measure to identify top key nodes. In both applications, the position value taking the Banzhaf value as a basis turns out to be more convincing than the Shapley-based approach.
The Soviet Home Front, 1941-1945: A Social and Economic History of the USSR in World War II
List of tables and maps Preface Acknowledgements Abbreviations and technical terms Part 1: On the Eve 1. Building Socialism 2. The Great Patriotic War 3. The State in Wartime Part 2: Soviet Society at War 4. Mobilisation 5. Subsistence and Survival 6. The Social Order Part 3: The Productive Effort 7. Fortress of the Rear 8. Labour: The 'Ultimate Bottleneck' 9. 'In Labour as in Combat' 10. Production: The Power of Victory 11. Planning: 'The Military-Economic Staff' Epilogue Tables Important dates References Maps Index