Two-Aggregate Games: Demonstration Using a Production–Appropriation Model

We expand the scope of the two-aggregate method by applying it to a situation in which many heterogeneous players are free to contribute to both aggregates. Such situations naturally arise in various resource allocation problems. Hence, our method is useful in many applications. A production–appropriation model is employed to illustrate how the problem of establishing the Nash equilibrium can be reduced from solving n>2 best-response functions in n unknowns to solving two consistency conditions in two unknowns. We then conduct a comparative static exercise that the conventional approach could not handle easily, if at all, to demonstrate the power of our method.