{"ID":2890053,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.19746","arxiv_id":"2507.19746","title":"Stackelberg stopping games","abstract":"We study a Stackelberg variant of the classical discrete-time Dynkin game, in which Player 1 (the leader) commits to a stopping strategy first and Player 2 (the follower) responds optimally. This leader-follower structure induces an optimal control problem for the leader and gives rise to intrinsic time-inconsistency. We first clarify notions of precommitment and equilibrium strategies in the Stackelberg setting, and contrast them with the Nash equilibrium in the standard Dynkin game using a finite-horizon example. We then consider an infinite-horizon framework with a time-homogeneous Markov process on a general Polish state space. We characterize the leader's value function under randomized precommitment strategies and show that randomized exact equilibrium strategies may fail to exist via a counterexample. Motivated by this nonexistence phenomenon, we introduce an entropy-regularized Stackelberg stopping game. The regularization induces a continuous response rule and yields the existence of randomized regular equilibria. We further show that these regular equilibria induce epsilon-equilibria for the original Stackelberg stopping game when the regularization parameter is sufficiently small. In the finite-state setting, we also establish a limiting result as the regularization parameter converges to zero.","short_abstract":"We study a Stackelberg variant of the classical discrete-time Dynkin game, in which Player 1 (the leader) commits to a stopping strategy first and Player 2 (the follower) responds optimally. This leader-follower structure induces an optimal control problem for the leader and gives rise to intrinsic time-inconsistency....","url_abs":"https://arxiv.org/abs/2507.19746","url_pdf":"https://arxiv.org/pdf/2507.19746v3","authors":"[\"Jingjie Zhang\",\"Zhou Zhou\"]","published":"2025-07-26T02:39:07Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}