Onesun Steve Yoo

Indexability of bandit problems with response delays

This article considers an important class of discrete time restless bandits, given by the discounted multiarmed bandit problems with response delays. The delays in each period are independent random variables, in which the delayed responses do not cross over. For a bandit arm in this class, we use a coupling argument to show that in each state there is a unique subsidy that equates the pulling and nonpulling actions (i.e., the bandit satisfies the indexibility criterion introduced by Whittle (1988). The result allows for infinite or finite horizon and holds for arbitrary delay lengths and infinite state spaces. We compute the resulting marginal productivity indexes (MPI) for the Beta-Bernoulli Bayesian learning model, formulate and compute a tractable upper bound, and compare the suboptimality gap of the MPI policy to those of other heuristics derived from different closed-form indexes. The MPI policy performs near optimally and provides a theoretical justification for the use of the other heuristics.

Optimal Time Allocation for Process Improvement for Growth-Focused Entrepreneurs

For many entrepreneurs, time is a key constraint. They need to invest time to achieve growth, but also lose time because of recurring crises. We develop a simple stochastic dynamic program to model how an entrepreneur should prioritize between improving processes to reduce crises versus harvesting revenue or ensuring future growth. We show that it is initially optimal to prioritize process improvement: an entrepreneur should strive for high process quality early in the venture’s growth process. We numerically analyze a simple heuristic derived from this optimal policy and identify the conditions under which it is (or is not) effective. It performs near optimally except when process quality or revenue rate may deteriorate too fast or when the cost of process improvement or revenue enhancement is too high. Our work provides a theoretical foundation for the advice found in the popular entrepreneurship and time management literature to invest time now to save time later.

The Time-Money Trade-Off for Entrepreneurs: When to Hire the First Employee?

For many early-stage entrepreneurs, hiring the first employee is a critical step in the firm’s growth. Doing so often requires significant time and monetary investments. To understand the trade-offs involved in deciding when to hire the first employee and how hiring differs in entrepreneurial settings from more established firm settings, we present a simple growth model that depends on two critical inputs for revenue generation: the entrepreneur’s time and money. We show that without hiring, the entrepreneur’s time eventually becomes more valuable than money in contributing to the firm’s growth. In that context, the value of the employee is driven by how much relief he provides to the entrepreneur. We characterize the optimal timing of hiring in terms of the firm’s cash position and how the firm is affected if it requires an upfront fixed investment in time and/or money. We find that the upfront investment in time needed for hiring cannot be converted to an equivalent upfront investment in money and that mistiming hiring can be very costly, especially when these upfront investments are high.

Consumer Choice and Market Outcomes Under Ambiguity in Product Quality

Facing purchase choice involving ambiguity in product quality, consumers behave in a boundedly rational manner. Consumers also exhibit varying degrees of predisposition toward a product. We present a simple model of boundedly rational choice under ambiguity. The model’s key feature is that it captures the interaction between predisposition and ambiguity. We build on the choice model to derive demand curves and the unique equilibrium market outcomes (regarding prices, profits, and market shares) under duopolistic competition. In equilibrium, market shares are proportional to prices. In symmetric competition, higher equilibrium prices obtain when the ambiguity in product quality is high or when the customer base is partisan. For vertically differentiated products, the strategy of a higher-quality firm to marginally reduce ambiguity depends on the ambiguity level inherent in the product–market environment. The presence of informed customers may increase the equilibrium prices and profits of both firms. An un...

Retention of capable new employees under uncertainty: Impact of strategic interactions

ABSTRACT We study a game involving a firm and a newly hired employee whose capability is initially unknown to both parties. Both players observe the performance of the employee and update their common posterior beliefs about the employee’s capability. The learning process presents each party with an option: the firm can terminate an incapable employee, and a capable employee can leave the firm for greater financial remuneration elsewhere. To understand the impact of this noncooperative interaction, we examine the Markov perfect equilibrium termination strategies and payoffs that unfold. We find that in the region of sufficiently high learning rates, reducing the rate of learning can increase the equilibrium payoff for both parties. Slower learning prolongs the employment because more performance outcomes must be observed to fully assess the employee’s capability. In the region of sufficiently slow learning rates, reducing the rate of learning can benefit the firm if the employee is deemed capable but hurt the firm otherwise. Our result identifies a nonfinancial way for firms to improve retention of capable new employees.

Time Allocation in Entrepreneurial Selling: Impact of Consumer Peer Learning and Incumbent Reaction

How should technology entrepreneurs allocate their time to potential customers? Considering two important dynamics that influence consumers’ purchase decisions regarding new technology products, consumer peer learning and incumbent reaction, we study the tactical-level time allocation decision with a simple game-theoretic model. We offer an economic rationale for the entrepreneurs optimal time allocation for different levels of consumer peer learning and incumbent reaction as well as different revenue distributions between the buyers, and we discuss theoretical and practical implications for technology entrepreneurship.

Employee Retention and Job Assignment Strategies of Entrepreneurial Firms under Uncertainty in Employee Capability

We study a game involving a firm and a newly hired employee whose capability is initially unknown to both parties. Both players observe the performance of the employee and update their common posterior beliefs about the employees capability. The learning process presents each party with an option: the firm can terminate an incapable employee, and a capable employee can leave the firm for greater financial remuneration elsewhere. To understand the impact of this noncooperative interaction, we examine the Markov perfect equilibrium termination strategies and payoffs that unfold. We find that in the region of sufficiently high learning rates, reducing the rate of learning can increase the equilibrium payoff for both parties. Slower learning prolongs the employment because more performance outcomes must be observed for assessing the employees capability. In the region of sufficiently slow learning rates, reducing the rate of learning can benefit the firm if the employee is deemed capable but hurt the firm otherwise. Our result identifies a nonfinancial way for firms to improve retention of capable new employees.