Classical Cooperative Theory I: Core-Like Concepts

Pure bargaining games discussed in the previous two lectures are a special case of n-person cooperative games. In the general setup coalitions other than the grand coalition matter as well. The primitive is the coalitional form (or, ``coalitional function'', or ``characteristic form''). The primitive can represent many different things, e.g., a simple voting game where we associate to a winning coalition the worth 1 and to a losing coalition the worth 0, or an economic market that generates a cooperative game. Von Neumann and Morgenstern (1944) suggested that one should look at what a coalition can guarantee (a kind of a constant-sum game between a coalition and its complement); however, that might not always be appropriate. Shapley and Shubik introduced the notion of a C-game (see Shubik (1982)): it is a game where there is no doubt on how to define the worth of a coalition. This happens, for example, in exchange economies where a coalition can reallocate its own resources, independent of what the complement does.