Implicit Centipedes

Sequential games are typically studied in environments where the game tree and payoffs are explicitly specified. In many real-world interactions, however, agents face implicitly formulated dynamic games: while the strategic structure and incentives are well defined, the underlying game form is not directly observed and must be inferred from experience. We study an implicitly formulated version of the centipede game and analyze a natural setting in which professional agents repeatedly engage in a sequential interaction with centipede-like incentives without observing the game tree. Using detailed intra-race data from Formula 1, we show that pit-stop timing decisions between closely competing drivers generate a centipede game once overtaking probabilities are taken into account. We estimate the payoff-relevant components of the game, compute the equilibrium of the resulting interaction, and compare theoretical predictions to observed behavior. We find that drivers respond strategically to each other: pit-stop timing shifts systematically when a nearby rival pits, even after controlling for tire degradation and race conditions. The observed responses broadly follow the equilibrium logic of the model. At the same time, we document substantial heterogeneity across teams: some teams consistently choose pit-stop timings close to the theoretical optimum, while others deviate substantially, and these patterns are associated with di!erences in success rates. By documenting equilibrium behavior in a complex sequential interaction outside the laboratory, the paper provides new evidence on how equilibrium predictions perform in natural dynamic environments.