Working Paper
An Endogenous Group Formation Theory of Co-operative Networks

This paper develops a theory of endogenous league formation and considers its implications for policy in developing countries. We generalize from features of the two most prominent European co-op leagues, Mondragón and La Lega, to develop the first formal model of the endogenous formation of co-operative networks and their constituent member coops. We show that if co-op leagues are formed through an open membership game, there can be two Nash equilibria, one with and one without a co-op league; and in this case, the equilibrium with a co-op league Pareto dominates the latter. In examining the formation of constituent co-operative firms, we show that, when payoffs to joining a co-op for potential worker members are initially increasing in membership and then decreasing, the outcome of the game depends on the rules of co-op formation. If payoffs are equal to the alternative wage at a single, unique membership size, then open membership and exclusive membership rules of the game yield the same outcome that either no co-op will be formed, or all co-ops formed will have the same number of members; but the coalition unanimity game has a unique outcome with co-op formation. If worker member payoffs exceed the alternative wage, our three alternative rules of co-op formation yield different outcomes. In the open membership game where some workers work for conventional firms, coops will be formed at the largest size for which co-op payoffs are equal to the alternative wage. However, if co-op payoffs exceed the conventional wage only when all workers join coops, then equilibrium co-op sizes can potentially include a wide range of membership sizes. In the exclusive membership game, all co-op sizes in the interval for which co-op payoffs are at least as large as conventional wages are equilibria. Finally, in the coalition unanimity game, only co-op sizes at which the highest income per member is achieved are equilibria. Only the latter result corresponds to the traditional neoclassical Ward-Vanek labour managed firm literature (though not necessarily with its comparative statics implications). A series of modelling extensions are discussed. Implications for existing and potential co-op leagues in developing countries are appraised, and implications for policy examined.