Efficient Mixed Clubs: Nonlinear-Pricing Equilibria with Entrepreneurial Managers

Scotchmer and Wooders (1987) show that efficient clubs are homogeneous when consumers are divisible in Berglas's (1976) anonymous crowding model. However, if consumers are not divisible or if clubs have multiple facilities with economies of scope, mixed clubs are efficient. In such a model, we consider clubs with multiple membership policies for different types of consumers, and show the existence and efficiency of equilibrium with nonlinear policies. We employ entrepreneurial equilibrium, an equilibrium concept with profit-seeking entrepreneurs. In our model, club managers and members of clubs care only about the members' actions, not their types. The equilibrium is efficient in our adverse selection model due to this "anonymity" of crowding effects. Our theorem can be regarded as showing the existence of a core allocation that satisfies envy-free property in the absence of nonanonymous crowding effects.