Optimal Single Threshold Stopping Rules and Sharp Prophet Inequalities

The paper characterizes sharp prophet inequalities for single threshold stopping rules as solutions to infinite two-person zero-sum games on the unit square with special payoff kernels. This game-theoretic formulation allows for the derivation of sharp non-asymptotic prophet inequalities for different classes of distributions and provides a simple and computationally tractable algorithmic paradigm for determining optimal single threshold stopping rules.