Cooperative game theory in law and economics

To analyse agreements between more than two parties, we take a slight detour and introduce the concept of a cooperative or coalitional game with transferable utility. Consider a set N of players, where we also denote the number of players by N > 2. A cooperative game with transferable utility or transferable payoffs consists of the following: [1]

The function v(S) is called the characteristic function. An allocation or imputation is simply a collection of payments x = [xt : i e N} to each of the participants in the cooperative game with xi > v({i}). An allocation is feasible if ^ x = v(N). In what follows we will assume that it is efficient for the grand coalition N to form. We say that the imputation x dominates y through S if there exists a coalition S such that:

We write x yS y if this is the case. In this situation, we also say that the allocation y is blocked by the coalition S.

  • [1] A set N > 2 of players or parties; • A function v(S) that represents the aggregate value or worth or benefitv(S) of each coalition or group of players S c N.
 
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