Real Switching Options and Equilibrium in Global Markets

This paper proposes and investigates a theoretical model in continuous time to analyze the real switching options that an economic entity in relationships with multiple external economic agents holds and the corresponding implications for equilibria between the entity and the agents if they are active. Although our basic model is generally applicable in several widely different economic scenarios, for expositional simplicity, we consider the specific problem of a firm and its global suppliers. We begin by considering the optimal dynamic policy problem for the firm where it may face different exogenously specified relationship specific fixed costs and random variable costs vis-à-vis each supplier and its goal is to dynamically choose a supplier over time so as to maximize its expected discounted cash flows. At any instant of time, the firm therefore holds compound real options of entering the market with a particular supplier, switching to another supplier or exiting the market. In the case where the firm has two suppliers, we derive necessary and sufficient conditions on the fixed and variable cost structures of the firm vis-à-vis the suppliers for the switching option of the firm to have strictly positive value. These also represent necessary and sufficient conditions for each supplier to have strictly positive expected cash flows. Either one of the two suppliers captures the market if these conditions do not hold. We illustrate our analytical results through several numerical simulations. Next, we investigate the equilibria between the firm and its suppliers when both suppliers are in the same foreign country (or, more generally, in two countries with pegged currencies) with uncertainty driven by fluctuations in the exchange rate process. The prices quoted by the suppliers and, therefore, the variable costs of the firm are now determined endogenously in equilibrium where the suppliers and the firm respond rationally and optimally to each other’s policies. We devise a procedure to derive equilibria between the firm and its suppliers where a leaderfollower game between two competing suppliers allows the firm to maximize value given its bargaining power. We provide sufficient conditions for both suppliers to co-exist in any possible equilibrium with the firm. We identify equilibria between the firm and its suppliers for several different values of underlying parameters that illustrate the impact of competition in global markets. JEL Classification Numbers: D21, D40, D80, G15, C73