🤖 AI Summary
This study addresses how an agent should dynamically allocate limited effort between novel and established solution approaches to maximize the probability of success when problem difficulty is unknown. By integrating Bayesian learning, dynamic optimization, and mechanism design theory, the authors formulate a principal–agent model that captures both the exploration–exploitation trade-off and moral hazard. The analysis reveals that the optimal policy alternates between trying new and existing methods, and that learning effects lead to front-loaded incentive schemes. These findings offer novel theoretical foundations for designing innovation strategies and dynamic incentives in creative endeavors such as scientific research and product development.
📝 Abstract
This paper studies how uncertainty about problem difficulty shapes problem-solving strategies. I develop a dynamic model where an agent solves a problem by brainstorming approaches of unknown quality and allocating a fixed effort budget among them. Success arrives from spending effort pursuing good approaches, at a rate determined by the unknown problem difficulty. The agent balances costly exploration (expanding the set of approaches) with exploitation (pursuing existing approaches). Failures could signal either a bad idea or a hard problem, and this uncertainty generates novel dynamics: optimal search alternates between trying new approaches and revisiting previously abandoned ones. I then examine a principal-agent environment, where moral hazard arises on the intensive margin: how the agent explores. Dynamic commitment leads contracts to frontload incentives, which can be counteracted by the presence of learning. The framework reflects scientific discovery, product development, and other creative work, providing insights into innovation and organizational design.