Contracting over multiple parameters: Capacity allocation in semiconductor manufacturing

This paper is a generalization of Mallik and Harker [Mallik, S., Harker, P.T., 2004. Coordinating supply chains with competition: Capacity allocation in semiconductor manufacturing. European Journal of Operational Research 159, 330–347] that presented an integrated model of incentive problems arising in forecasting and capacity allocation. In that model, multiple product managers and multiple manufacturing managers forecast the means of their respective demand and capacity distributions, and a central coordinator allocates capacities based on these forecasts. A mechanism that elicits truthful information from the managers was the main contribution of that paper. The objective of this paper is to generalize our previous results to multiple statistics reporting. This work assumes that the central coordinator can ask the managers to report multiple statistics (mean and variance, for example) about their respective distributions. We propose a game theoretic model and design a mechanism (a bonus scheme and an allocation rule) that elicits truthful reporting of all statistics by all managers. It turns out that the structure of the optimal bonus schemes are rather simple with easily calculable parameters. We also show that a large class of allocation rules are manipulable. A bonus is often required for elicitation of truthful information. We compare our results of multiple statistics reporting with those from Mallik and Harker (2004). We also characterize under what conditions the reporting of the extra information is of limited use.