Coalition Formation in Political Games

We study the formation of a ruling coalition in political environments. Each individual is endowed with a level of political power. The ruling coalition consists of a subset of the individuals in the society and decides the distribution of resources. A ruling coalition needs to contain enough powerful members to win against any alternative coalition that may challenge it, and it needs to be self-enforcing, in the sense that none of its subcoalitions should be able to secede and become the new ruling coalition. We first present an axiomatic approach that captures these notions and determines a unique self-enforcing ruling coalition. We then construct a simple dynamic game that encompasses these ideas and propose the notion of sequentially weakly dominant equilibrium as an equilibrium concept. We prove that this dynamic game generically has a unique sequentially weakly dominant equilibrium, and this equilibrium coincides with a particular type of trembling hand perfect equilibrium. We then show the equivalence of these equilibria to the self-enforcing ruling coalition emerging from the axiomatic approach and also to the core of a related non-transferable utility cooperative game. The substantive conclusions of our analysis relate to the structure of ruling coalitions. The nature of the ruling coalition is determined by the power constraint, which requires that the ruling coalition be powerful enough, and by the enforcement constraint, which imposes that no subcoalition of the ruling coalition that commands a majority is self-enforcing. The major insight that emerges from this characterization is that the coalition is made self-enforcing precisely by the failure of its winning subcoalitions being self-enforcing. This is most simply illustrated by the following simple finding: with majority rule, while three-person (or larger) coalitions can be self-enforcing, two-person coalitions are generically not self-enforcing. Therefore, the reasoning in this paper suggests that three-person juntas or councils should be much more common than two-person ones. In addition, we provide conditions under which the grand coalition will be the ruling coalition and conditions under which the most powerful individuals will not be included in the ruling coalition. We also use this framework to discuss endogenous party formation.