Equilibrium in fiscal competition games from the point of view of the dual

Papers that examine fiscal competition for mobile factors of production commonly employ simultaneous move games between two states and focus on the inefficiency of the equilibria. Most often, the existence of the equilibrium is left unexplored. By examining decision making by governments that make only constrained efficient choices, we derive sufficient conditions for the existence of equilibria when there are multiple policy instruments, multiple mobile factors and many different production processes. Convexity of the minimum cost function, "dual" to the factor preferences and production function primitives, is sufficient to ensure the existence of equilibrium. We also find that equilibrium may not exist because of the economies of scale inherent in provision of public goods which benefit mobile factors.