Chapter 14: Coalitional Play
14. Coalitional play The previous two chapters have focused primarily on a cooperative analysis of games in partition function form, taking the partition functions as givens. This chapter will discuss the determination of partition functions by non-cooperative play among coalitions. Thus we build a link between the cooperative and non-cooperative aspects of interdependent decisions. As Aumann (2003, p. 6) has observed, “those two aspects of game theory are really not two separate disciplines, they are part of the same whole.” For the purposes of public policy, though, it is not enough that cooperative and non-cooperative analyses are complementary, as Aumann observes. Rather, we need analyses of given models that are linked, drawing on both cooperative and non-cooperative approaches. This reflects the (often) different roles of cooperative and non-cooperative models in the pragmatic project of public policy, in that it is commonly the non-cooperative models that identify the problems, so that cooperative analysis of the same examples is necessary in order to propose solutions. Several examples will be given to illustrate the link and the application of the analysis begun in Chapter 10. 14.1 PARTITION FUNCTIONS AND COALITIONAL PLAY In general, the value of a coalition is determined by the value that it can obtain by its own efforts acting separately. Accordingly (as argued in Chapter 10) the Nash equilibrium, or some appropriate refinement or extension of it, will determine the values of embedded coalitions. That is, the partition function is determined by coalitional play. In the simplest case, the strategies...
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