Incentive Design for Operations-Marketing Multitasking
Christopher Thomas Ryan
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A firm hires an agent (e.g., store manager) to undertake both operational and marketing tasks. Marketing tasks boost demand, but for demand to translate into sales, operational effort is required to maintain adequate inventory. The firm designs a compensation plan to induce the agent to put effort into both marketing and operations while facing “demand censoring” (i.e., demand in excess of available inventory is unobservable). We formulate this incentive-design problem in a principal-agent framework with a multitasking agent subject to a censored signal. We develop a bang-bang optimal control approach, with a general optimality structure applicable to a broad class of incentive-design problems. Using this approach, we characterize the optimal compensation plan, with a bonus region resembling a “mast” and “sail,” such that a bonus is paid when either all inventory above a threshold is sold or the sales quantity meets an inventory-dependent target. The optimal “mast and sail” compensation plan implies non-monotonicity, where the agent can be less likely to receive a bonus for achieving a better outcome. This gives rise to an ex post moral hazard issue where the agent may “hide” inventory to earn a bonus. We show this ex post moral hazard issue is a result of demand censoring. If available information includes a waitlist (or other noisy signals) to gauge unsatisfied demand, no ex post moral hazard issues remain.