5 - Values of cooperative games
Published online by Cambridge University Press: 05 January 2013
Summary
Overview
The most ambitious task of cooperative game theory is to build a universal solution concept based on widely acceptable equity axioms, picking out of every cooperative game a unique utility distribution, just as the social choice function of Chapter 3 does. Such an object is called a value, or value operator. For more than 30 years, this viewpoint has been tested for TU games. By and large, it proves to be successful. Surely, no single solution concept has emerged that would satisfy everyone's sense of equity for all TU games. All the same, no single social choice function is the universal panacea of axiomatic bargaining (see Part I). However, two prominent values have been discovered and prove useful in a wide range of economic models. These are the Shapley value and the nucleolus, to which most of the discussion of this chapter is devoted.
In a nutshell, the nucleolus applies egalitarianism to TU games, whereas the Shapley value follows from a utilitarian principle. Indeed, the nucleolus minimizes the leximin SWO over long utility vectors in which every coordinate corresponds to a different coalition (see Definition 5.4). The Shapley value, on the other hand, renumerates each agent by averaging his marginal contributions to all coalitions containing him; it is utilitarian inasmuch as classical utilitarianism (Chapter 1) is likewise based upon average utility. Accordingly, the nucleolus tends to be harder to compute than the Shapley value (just as maximizing the leximin SWO is a more involved program than maximizing the utilitarian one).
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- Axioms of Cooperative Decision Making , pp. 107 - 142Publisher: Cambridge University PressPrint publication year: 1988