Burden Sharing and Public Good Provision: A Numerical Sensitivity Analysis

This paper reports on our numerical analysis of the model developed in Rausser-Simon 1991a and 1991b. We will assume that the reader is thoroughly familiar with the latter paper and refer frequently to the terminology introduced there. Two conclusions were readily apparent from the paper. First, many of the more interesting comparative statics questions we want to ask about the model are unlikely to have simple and determinate answers. In particular, it is especially difficult to determine the impact on alliance performance of certain kinds of changes in the spatial configuration and distribution of power within the alliance. The reason is that the fortunes of different alliance members are intertwined in highly intricate ways. Distributional changes set off a chain of conflicting events that are extremely difficult to disentangle. A second observation is that even when determinate comparative statistics results can be obtained, it may be imprudent to assign much significance to them. The method of comparative statics involves infinitesimal changes in parameters, but the effects of such changes may be quite different from the effects of even small, finite changes. Of course, this comment applies generally to all comparative statics, but the problem is exacerbated in our case by the highly discontinuous nature of our model. Whenever a change in some parameter leads some player in some round of negotiations to choose a different coalition, there will generally be a discontinuity in each player's playoff function. Moreover, coalition choice is intrinsic to the problem at hand: in our view, any model that denies participants the opportunity to consider alternative coalitions cannot be considered a genuine model of multilateral bargaining. We conclude that these discontinuities are an unavoidable aspect of the problem at hand and cannot be assumed away.