Do the world’s best tennis pros play Nash equilibrium mixed strategies? We answer this question using data on serve-direction choices (to the receiver’s left, right, or body) from the Match Charting Project. Using a new approach, we test and reject a key implication of a mixed-strategy Nash equilibrium: that the probability of winning the service game is identical for all possible serve strategies. We calculate best-response serve strategies by dynamic programming (DP) and show that for most elite pro servers, the DP strategy significantly increases their win probability relative to the mixed strategies they actually use.

We introduce a computationally tractable dynamic equilibrium model of automobile markets with heterogeneous consumers, focused on stationary flow equilibria. We introduce a fast, robust algorithm for computing equilibria and use it to estimate a model using nearly 39 million observations on car ownership transitions from Denmark. The estimated model fits the data well, and counterfactual simulations show that Denmark could raise total tax revenue by reducing the new-car registration tax rate. We show that reducing this tax rate while raising the tax rate on fuel increases aggregate welfare, tax revenue, and car ownership, while reducing car ages, driving, and CO2 emissions.