Collaboration in contingent capacities with information asymmetry

We study the optimal contracting problem between two firms collaborating on capacity investment with information asymmetry. Without a contract, system efficiency is lost due to the profit-margin differentials among the firms, demand uncertainty, and information asymmetry. With information asymmetry, we demonstrate that the optimal capacity level is characterized by a newsvendor formula with an upward-adjusted capacity investment cost, and no first-best solution can be achieved. Our analysis shows that system efficiency can always be improved by the optimal contract and the improvement in system efficiency is due to two factors. While the optimal contract may bring the system's capacity level closer to the first-best capacity level, it prevents the higher-margin firm from overinvesting and aligns the capacity-investment decisions of the two firms. Our analysis of a special case demonstrates that, under some circumstances, both firms can benefit from the principal having better information about the agent's costs.