# 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 = *[x _{t}* :

*i e N*} to each of the participants in the cooperative game with

*x*v({i}). An allocation is

_{i}>*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 y _{S} 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.