Search Strategies in the Game with a Team of Pursuers and One Evader on the Plane

Authors

  • Semyon V. Mestnikov North-Eastern Federal University
  • Nikolay V. Petrov North-Eastern Federal University

DOI:

https://doi.org/10.21638/11701/spbu31.2020.18

Abstract

We consider a differential simple search game without phase constraints on the plane. Each pursuer from the team chooses an initial position and piecewise constant strategy. As an example, the game of simple search of immobile hider (evader) on the plane is considered, and the necessary conditions for detection are found. For cases with two and three pursuers, a comparison of the detection time of the evader was made and approximate information sets numerically constructed.

Keywords:

differential search game, information set, the pursuer team, numerical construction, comparison of detection time

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References

Petrosjan, L. A., Zenkevich, N. A. (1986). Optimal Search in conflict condition. St.-Peterbg. Gos. Univ.: St. Petersburg (in Russian)

Zenkevich, N. A., Mestnikov, S. V. (1991). Dynamical search of a moving object in conflict condition. Leningrad Univ., Voprosy Mekh. Protsess. Upravl., 14, 68–76: St. Petersburg (in Russian)

Petrosjan, L. A., Garnaev, A. Yu. (1992). Search games. St.-Peterbg. Gos. Univ.: St. Petersburg (in Russian)

Mestnikov, S. V. (1994). Estimates for the detection probability and uncertainty domain in a differential search game. YaGU, Math. notes of YaGU, 3, 99–104: Yakutsk (in Russian)

Mestnikov, S. V. (2002). Approximation of the information set in a differential search game with a team of pursuers. 10th international symposium on dynamic games and applications. St. Petersburg, Russia. In 2 vol. St. Petersburg: International Society of Dynamic Games, St. Petersburg State Univ., 630–631 : St. Petersburg

Mestnikov, S. V., Petrov, N .V., Everstova, G. V. (2014). Numerical Construction of the Information Sets in the Simple Search Game with a team of pursuers and Estimates for a Detection Probability. Collected abstracts of papers presented on the Eighth International Conference Game Theory and Management / Editors Leon A. Petrosyan and Nikolay A. Zenkevich. St.Peterburg. Graduate School of Management SPbU, 207–208

Honzaki, R. (2016). Search Games: Literature and survey. J. Oper. Rec. Soc. Japan, 59(1), 1–34

Mestnikov, S. V., Petrov, N .V. (2017). Numerical Construction of the Information Sets and Sufficient Conditions for k-detection in the Simple Search Game on the Plane. NEFU, Mathematical Notes of NEFU, 4, 13–29: Yakutsk (in Russian)

Mestnikov, S. V., Petrov, N. V. (2018). Numerical Construction of the Information Sets and Optimization of Detection Time in the Simple Search Game with Team of Pursuers on the Plane.(English) Collected abstracts of papers presented on the Twelfth International Conference Game Theory and Management (GTM2018) / Editors Leon A. Petrosyan and Nikolay A. Zenkevich. SPb.: Graduate School of Management SPbU, 2018, 111–112

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Published

2022-02-03

How to Cite

Mestnikov, S. V., & Petrov, N. V. (2022). Search Strategies in the Game with a Team of Pursuers and One Evader on the Plane. Contributions to Game Theory and Management, 13. https://doi.org/10.21638/11701/spbu31.2020.18

Issue

Vol. 13 (2020)

Section

Articles

License

Articles of "Contributions to Game Theory and Management" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.