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SIAM Journal on Control and Optimization
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This paper considers two independent firms that invest in resources such as capacity or inventory based on imperfect market forecasts. As time progresses and new information becomes available, the firms update their forecasts and have the option to trade their resources. The trade contract is determined as the bargaining equilibrium or, alternatively, as the price equilibrium. Assuming a fairly general form of the profit functions, we characterize the Nash equilibrium investment levels, which are first-best under the price equilibrium trade contract, but not under the bargaining equilibrium trade contract. To gain additional insights, we then focus on firms that face stochastic demand functions with constant price elasticity and have contingent pricing power. Assuming a general forecast evolution process, we characterize the impact of the option to trade and the firms' cooperation on equilibrium investments, expected prices, profits, and consumer surplus. Finally, to study the main driving forces of trading, we employ a well-established and empirically tested forecast updating model in which the forecast evolution process follows a two-dimensional geometric Brownian motion. Under this model, we prove that the equilibrium investments, expected prices, profits, and consumer surplus are nondecreasing in the quality and timing of forecast revisions, in market variability, and in foreign exchange volatility, but are nonincreasing in market correlation.