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A Dijkstra-Type Algorithm for Dynamic Games

Author

Listed:
  • Martino Bardi

    (Università degli Studi di Padova)

  • Juan Pablo Maldonado López

    (Sorbonne Universités
    Univ Paris-Diderot)

Abstract

We study zero-sum dynamic games with deterministic transitions and alternating moves of the players. Player 1 aims at reaching a terminal set and minimizing a possibly discounted running and final cost. We propose and analyze an algorithm that computes the value function of these games extending Dijkstra’s algorithm for shortest paths on graphs. We also show the connection of these games with numerical schemes for differential games of pursuit-evasion type, if the grid is adapted to the dynamical system. Under suitable conditions, we prove the convergence of the value of the discrete game to the value of the differential game as the step of approximation tends to zero.

Suggested Citation

  • Martino Bardi & Juan Pablo Maldonado López, 2016. "A Dijkstra-Type Algorithm for Dynamic Games," Dynamic Games and Applications, Springer, vol. 6(3), pages 263-276, September.
    • Handle: RePEc:spr:dyngam:v:6:y:2016:i:3:d:10.1007_s13235-015-0156-0
    DOI: 10.1007/s13235-015-0156-0
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    References listed on IDEAS

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    1. L. Grüne & O. Junge, 2008. "Global Optimal Control of Perturbed Systems," Journal of Optimization Theory and Applications, Springer, vol. 136(3), pages 411-429, March.
    2. Alexander Vladimirsky, 2008. "Label-Setting Methods for Multimode Stochastic Shortest Path Problems on Graphs," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 821-838, November.
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