Dynamic Games and Applications

, Volume 6, Issue 3, pp 263–276 | Cite as

A Dijkstra-Type Algorithm for Dynamic Games

Article

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.

Keywords

Zero sum dynamic games Dijkstra algorithm Pursuit evasion games Discrete time games 

Mathematics Subject Classification

91A25 65Kxx 49N70 91A23 91A24 49N75 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità degli Studi di PadovaPaduaItaly
  2. 2.UPMC Univ Paris 06, CNRS, UMR 7586, IMJ-PRGSorbonne UniversitésParisFrance
  3. 3.Sorbonne Paris Cité, UMR 7586Univ Paris-DiderotParisFrance

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