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Optimal Feedback in a Dynamic Game of Generalized Shortest Path

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Advances in Dynamic Games

Part of the book series: Annals of the International Society of Dynamic Games ((AISDG,volume 8))

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Abstract

We consider the problem of generalized shortest path. The task is to transit optimally from the origin through a system \( M_i ,i \in \overline {1,m} \), of intermediate sets in ℝd to a fixed destination point (or set), under conditions that only one node in M i can be chosen for passing. Any returns to the sets that have already been passed, are prohibited. The (combinatorial) cost function to minimize is either additive or bottleneck. The visiting nodes \( x_i \in M_i ,i \in \overline {1,m} \), are either governed by an antagonistic nature or by a rational antagonist. For this multistage game problem both open-loop and feedback settings are suggested. The feedback problem is posed in the class of feedback strategies which can change route during motion, depending on the current moves of the opponent. They provide, in general, a strictly better value of the problem, with respect to the open-loop minimax setting. The optimal feedback minimax strategy is constructed, and some (polynomial)heuristics are given.

This research was supported by the RF Ministry of Education under Grant E02-1.0-232.

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Authors and Affiliations

  1. Ural Polytechnic Institute, Ekaterinburg, Russia

    Vyacheslav P. Serov

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  1. Vyacheslav P. Serov
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Editors and Affiliations

  1. ORDECSYS, Place de l’Etrier 4, Chêne-Bougeries, CH-1224, Switzerland

    Alain Haurie

  2. Graduate School of Decision Science and Technology, Tokyo Institute of Technology, 2-12-1 Ookayama, Tokyo, 152-8552, Japan

    Shigeo Muto

  3. Faculty of Applied Mathematics and Control Processes, State University of St. Petersburg, 198504, St. Petersburg, Russia

    Leon A. Petrosjan

  4. Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, IL, 60607-7045, USA

    T. E. S. Raghavan

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Serov, V.P. (2006). Optimal Feedback in a Dynamic Game of Generalized Shortest Path. In: Haurie, A., Muto, S., Petrosjan, L.A., Raghavan, T.E.S. (eds) Advances in Dynamic Games. Annals of the International Society of Dynamic Games, vol 8. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4501-2_3

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