Interdependent Hitting Times

2026-06-04

AI Summary

This study addresses the identification and estimation of equilibrium outcomes in synchronous games from interdependent stopping time data. The equilibrium is modeled as a system of mutually dependent first-passage times, wherein an individual’s incentive to stop intensifies as others cease activity, and payoffs are influenced by common shocks as well as both observed and unobserved heterogeneity. A key innovation lies in the use of spectrally negative Lévy processes to characterize common shocks, which facilitates nonparametric identification of the model. Building on this foundation, the authors develop a computationally tractable estimation framework that combines maximum simulated likelihood with simulated method of moments. Monte Carlo experiments demonstrate strong finite-sample performance, offering the first empirical tool for synchronous games that simultaneously ensures rigorous identification and computational feasibility.

Abstract

This paper studies interdependent durations as equilibrium outcomes of a synchronization game, a continuous-time stopping game in which the incentive to stop increases when other players stop. We allow the payoffs to vary with both common shocks and observed and unobserved agent characteristics. The common shocks follow a spectrally negative Lévy process, a semiparametric process that includes Brownian motion as a special case but may also have jumps. We show that equilibrium outcomes can be represented as interdependent hitting times and use this to establish the game's nonparametric identification from data on stopping times and covariates. We develop maximum simulated likelihood and method of simulated moments estimators and evaluate their finite-sample and computational performance in Monte Carlo experiments. The results provide a tractable framework for identifying and estimating synchronization games from interdependent duration data.

Problem

• interdependent durations
• synchronization game
• hitting times
• common shocks
• equilibrium identification

Innovation

• interdependent hitting times
• synchronization game
• spectrally negative Lévy process
• nonparametric identification
• simulated estimation