Management Science · 2025 · Suren Basov、Nisvan Erkal、Deborah Minehart、Suzanne Scotchmer
中文摘要
本文考察一个区分想法与创新的创新模型。尽管创新会对激励作出反应，想法却是一种稀缺资源，对创新速度构成外生约束。我们研究最优奖励结构如何受想法稀缺性的塑造。模型中作为创新替代的想法在随机时刻到达随机的接收者。通过放弃对当前想法的投资，社会保留了（延迟之后）对同一市场利基投资于更好想法的选择权。由于相继出现的想法可能为不同的人所想到，私人最优与社会最优之间存在冲突。社会计划者观察不到想法的到达，只能随时间推移了解想法的到达率。我们用一般形式的连续密度函数刻画社会计划者的信念，并说明信念的演化可以借助累积风险函数加以追踪。社会计划者设定的奖励具有双重目的：了解想法的到达率，以及在更低的延迟与成本更低的想法之间进行权衡。我们证明，最优奖励随时间推移而提高，因为社会计划者逐渐认为想法更为稀缺。
Abstract
We consider a model of innovation that distinguishes between ideas and innovations. Although innovation responds to incentives, ideas are a scarce resource that provides an exogenous constraint on the rate of innovation. We investigate how the optimal reward structure is shaped by the scarcity of ideas. Substitute ideas for innovation in the model arrive to random recipients at random times. By forgoing investment in a current idea, society preserves an option to invest in a better idea for the same market niche but with delay. Because successive ideas may occur to different people, there is a conflict between private and social optimality. The social planner does not observe the arrival of ideas and learns over time about the arrival rate of ideas. We represent the social planner’s beliefs using a general continuous density and illustrate that the evolution of beliefs can be tracked by the cumulative hazard function. The reward set by the social planner serves a dual purpose: learning about the arrival rate of ideas and trading off lower delays against lower-cost ideas. We show that the optimal reward increases as time passes because the social planner comes to view ideas as more scarce.