Complete Solution of the Lady in the Lake Scenario
Document Type
Article
Publication Date
1-3-2025
Abstract
In the Lady in the Lake scenario, a mobile agent, L, is pitted against an agent, M, who is constrained to move along the perimeter of a circle. L is assumed to begin inside the circle and wishes to escape to the perimeter with some finite angular separation from M at the perimeter. This scenario has, in the past, been formulated as a zero-sum differential game wherein L seeks to maximize terminal separation and M seeks to minimize it. Its solution is well-known. However, there is a large portion of the state space for which the canonical solution does not yield a unique equilibrium strategy. This paper provides such a unique strategy by solving an auxiliary zero-sum differential game. In the auxiliary differential game, L seeks to reach a point opposite of M at a radius for which their maximum angular speeds are equal (i.e., the antipodal point). L wishes to minimize the time to reach this point while M wishes to maximize it. The solution of the auxiliary differential game is comprised of a Focal Line, a Universal Line, and their tributaries. The Focal Line tributaries' equilibrium strategy for L is semi-analytic, while the Universal Line tributaries' equilibrium strategy is obtained in closed form.
DOI
10.1007/s13235-024-00614-2 ; arXiv: 2401.14994
Source Publication
Dynamic Games and Applications (ISSN 2153-0785 | e-ISSN 2153-0793)
Recommended Citation
Von Moll, A., Pachter, M. Complete Solution of the Lady in the Lake Scenario. Dyn Games Appl (2025). https://go.openathens.net/redirector/afit.edu?url=https://doi.org/10.1007/s13235-024-00614-2
arXiv preprint as linked from AFIT Scholar:
Von Moll, A., & Pachter, M. (2024). Complete solution of the Lady in the Lake scenario (arXiv:2401.14994 [math.OC]). arXiv e-print repository. https://doi.org/10.48550/arXiv.2401.14994.
Comments
This article was published by Springer online ahead of inclusion in an issue of Dynamic Games and Applications. The published version of record is accessible by subscription though the DOI link on this page.
The "Link to Full Text" on thnis page opens the preprint version hosted at the arXiv.org repository. It is licensed as an open access eprint, free of all copyright, and may be freely reproduced, distributed, transmitted, modified, built upon, or otherwise used by anyone for any lawful purpose. The preprint is made available under the Creative Commons public domain dedication (CC0), which waives all copyright.
Please provide proper credit to the authors in any re-use.