The game-theoretic formulation developed in the paper can be extended to more general classes of stopping rules by considering a broader range of decision-making strategies. While the paper focuses on single threshold stopping rules, one can incorporate more complex stopping rules that involve multiple thresholds, randomized decisions, or other decision-making mechanisms. By expanding the set of possible stopping rules, the game-theoretic approach can provide insights into the optimal strategies for a wider range of scenarios. This extension may involve defining new pay-off functions, considering different constraints, or exploring alternative solution concepts in game theory to analyze the interactions between decision makers and nature in the stopping problem.