This case presents a dilemma that professional golfers face when having to choose a target point for landing the ball. Key to this case is to acknowledge uncertainty as reflected in less-than-perfect accuracy. Thus the ball will land in a ""cloud"" around the intended target. On such a cloud, some spots (e.g., the fairway) are better than others (e.g., sand bunkers or rough). There is therefore a conflict between advancing the ball as close to the hole as possible, while at the same time reducing the chance of being in trouble on the next shot. The idea is to find a sweet spot between these two competing goals. To operationalize this problem, we use data from the Professional Golfers' Association (PGA) tour to estimate the average number of shots to complete the hole as a function of (i) distance to the hole, and (ii) type of surface (fairway, rough, recovery, sand, or the green). The case comes with a companion Excel spreadsheet, UVA-QA-0953X, which shows a map of a classical hole in the PGA Tour (the 10th at the Riviera Country Club in Los Angeles). This Excel file also displays a heat map of a bivariate normal around any chosen target, and a heat map with the average number of strokes to complete the hole. Students' goal is to understand the model and use it to find a good target.
This technical note introduces dynamic programming (DP), a powerful tool for finding optimal solutions to complex problems that involve a concatenation of multiple decisions. This note assumes some familiarity with decision trees. Compared to decision trees, DP simplifies the problem representation by pooling together similar decision situations, allowing us to apply backward induction in batches by means of the Bellman equation. The note stresses the importance of data to estimate transition probabilities, as well as to proxy the value-to-go in some complex situations. The note includes four exercises, which are supported by spreadsheets for both students and instructors. These cover job search decisions, pricing of American options, and hotel pricing (revenue management).
This note discusses a variety of methods to assist intuition in complex situations with multiple objectives and a potentially large set of alternatives. It begins with heuristic rules, which are relatively simple ways to sort out alternatives without thinking too much about trade-offs. After discussing the reliability of such rules, it moves to multicriteria analysis, which is a more rational method of balancing conflicting objectives.
This case describes the situation of Tesla, Inc. (Tesla), in mid-2019. Tesla had just successfully launched the more affordable Model 3, but sales of the most expensive and profitable Models X and S were stagnant. In order to incentivize the sales of these luxury models, Tesla recently brought back free Supercharging for life for customers purchasing Models X or S. The case provides information about the history of Tesla, one customer's hesitation about buying a Tesla electric vehicle (EV), purchasing prices, different ways to procure electricity and their cost, Supercharging stations, tax credits, and the autonomous and self-driving features of the car.
An investor, Janice Zhuk, examines Tesla's quarterly safety data that includes the number of miles it took to register one accident among Tesla cars driving with autopilot versus those without autopilot. The data set is small, so the validity of any statistical analysis may be compromised. The data allow one to run a simple t-test comparison of means. Because of the small sample size, the case invites a discussion on the hypothesis of the regression model, in particular, the normality of the residuals.
When a consumer purchases an item, the presumption is that the benefit obtained from it exceeds the price paid-we can think of this difference as the consumer profit. How do consumers calculate this profit, especially when they do not immediately consume the purchased item? This technical note presents a model of mental accounting that gives insights into the process that consumers follow to calculate value. It compares rational logic, accounting logic, and mental accounting logic, incorporating the phenomena of loss aversion, transaction utility, and consumer anomalies. This note is used at Darden in the second-year "Behavioral Decision Making" course. It would also be suitable in courses covering rational decision making in business.
Individuals' judgement of probabilities-the likelihood of different events to occur, or the attribution of likely causes to what has occurred-is plagued by numerous biases and errors. This note focuses on Bayesian updating and the base rate neglect, and also provides a brief overview of other biases, including overconfidence, reversion to the mean, the law of small numbers, the conjunction fallacy, confirming evidence bias, hindsight bias, and the conjunction fallacy. Numerous examples illustrate the implications of the biases for managerial decisions.
Many decisions involve trade-offs between present and future costs and benefits. We procrastinate difficult tasks, and we forgo larger rewards for smaller ones if we can get them sooner. Why do we change our minds about the value of upcoming events? The traditional discounting model, which predicts how individuals discount future consequences and resolve trade-offs between present and future costs and benefits, does not account for this observed behavior. The behavioral discounting model presented in this technical note accounts for observed behaviors by incorporating patterns of overall high discounting, magnitude effects, and decreasing impatience.
This case describes a common situation in old buildings, namely the decision as to whether intall an elevator. In this armchair case, we have an apartment building in Budapest with 3 towers, each containing 24 homeowners, with a possible interest in adding an elevator to each tower of the walk-up building. The case begins by discussing serveral ways to fairly distribute the cost if the elevators are approved. One way is an equal split. The second way is to have the homeowners living on higher levels pay more. A formula that effectively implements the Shapley value is proposed. Next, the case describes the pivot mechanism as a way to bypass the free riding problem that would arise if homeowners were simply asked about their willingness to pay. The question for discussion is whether the homeowners would agree to use the pivot mechanism. In particular, how to explain to the homeowners the penalties that would result from implementing the mechanism and how those penalties are applied to those homeowners who are pivotal. The challenge for students is how to market the pivotal mechanism.
MBA students are taught to use the expected monetary value (EMV) to evaluate risky opportunities. The reaction of individuals to risk, however, is far more complex. In fact, individuals are rarely found to be consistently risk neutral, risk averse, or risk seeking. They can be all these things, depending on whether the probabilities are small or large or the outcomes are gains or losses. The purpose of this note is to introduce a behavioral model that modifies EMV and does a better job of predicting how individuals evaluate risky prospects. The model builds on the distinction between probabilities and decision weights, as well as the notion of framing and loss aversion, as put forward by prospect theory.