Multiplayer Stopping Games with a Conditionally Atomless Filtration
Abstract
Stopping games are the multiplayer generalization of optimal stopping problems, in which each player independently chooses when to stop, and the payoff depends on who stops first and when. While the existence of ε-equilibria in two-player stopping games with integrable payoffs is known, the multiplayer case has remained open. We prove that every multiplayer stopping game in discrete time with integrable payoff process admits an ε-equilibrium for every ε > 0, provided the filtration is conditionally atomless. This condition is satisfied, in particular, when the underlying probability space is {0,1}dN endowed with the uniform measure and its natural filtration. Our method also shows that every three-player stopping game, without the restriction to conditionally atomless filtration, admits an ε-equilibrium, for every ε > 0. The proof combines techniques developed for two-player stopping games and for multiplayer quitting games, with a key new insight: the richness encoded in a conditionally atomless filtration can substitute for an external public randomization device, allowing players to coordinate without an explicit coordination signal.
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BibTeX
@misc{simon2026multiplayer,
title = {{Multiplayer Stopping Games with a Conditionally Atomless Filtration}},
author = {Robert Samuel Simon and Eilon Solan and Grzegorz Tomkowicz},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07184},
eprint = {2611.07184},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07184},
}
RIS
TY - UNPB
TI - Multiplayer Stopping Games with a Conditionally Atomless Filtration
AU - Robert Samuel Simon
AU - Eilon Solan
AU - Grzegorz Tomkowicz
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.07184
UR - https://arxiv.org/abs/2611.07184
AB - Stopping games are the multiplayer generalization of optimal stopping problems, in which each player independently chooses when to stop, and the payoff depends on who stops first and when. While the existence of ε-equilibria in two-player stopping games with integrable payoffs is known, the multiplayer case has remained open. We prove that every multiplayer stopping game in discrete time with integrable payoff process admits an ε-equilibrium for every ε > 0, provided the filtration is conditionally atomless. This condition is satisfied, in particular, when the underlying probability space is {0,1}^dN endowed with the uniform measure and its natural filtration. Our method also shows that every three-player stopping game, without the restriction to conditionally atomless filtration, admits an ε-equilibrium, for every ε > 0. The proof combines techniques developed for two-player stopping games and for multiplayer quitting games, with a key new insight: the richness encoded in a conditionally atomless filtration can substitute for an external public randomization device, allowing players to coordinate without an explicit coordination signal.
ER -