Coalitional Stability of a "Bipolar World"

The model considered in the paper is devoted to the analysis of local public good provision in the economy the consumers of which are exogenously divided to a finite number of types. Each type is represented by a continuum of identical agents and is described by a certain optimal bundle of characteristics of a public good to be consumed; departure from the optimal point in the space of characteristics involves an extra cost for each individual. Masses of consumers of each type are also exogenous to the model. A solution concept is introduced which is a partition of the set of individuals into disjoint groups, a priori without correlation to the division into types. Each group has access to one and the same variety of a local public good, the latter being selected via the median principle, i.e. minimizing total "disagreement cost" of members of that group. Partition is coalitionary stable if no coalition (i.e. nonempty measurable subset) of agents can Pareto improve itself via the formation of a new jurisdiction and choosing a variety of a good according to the same median principle. The case of the two types of consumers is fully analyzed. For each configuration of parameters of the model, all stable partitions are specified. It turns out that, for certain combinations of parameters, there are no stable partitions, and which could be even more surprising, there exist economies for which the only stable partition divides one of the two types between the two groups. Such a situation is impossible if one looks for optimal, not stable, solutions.