NUMERICAL METHODS FOR DIFFERENTIAL GAMES BASED ON PARTIAL DIFFERENTIAL EQUATIONS

M. Falcone ()
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M. Falcone: Dipartimento di Matematica, Università di Rome, "La Sapienza", P. Aldo Moro 2, 00185 Rome, Italy

International Game Theory Review (IGTR), 2006, vol. 08, issue 02, 231-272

Abstract: In this paper we present some numerical methods for the solution of two-persons zero-sum deterministic differential games. The methods are based on the dynamic programming approach. We first solve the Isaacs equation associated to the game to get an approximate value function and then we use it to reconstruct approximate optimal feedback controls and optimal trajectories. The approximation schemes also have an interesting control interpretation since the time-discrete scheme stems from a dynamic programming principle for the associated discrete time dynamical system. The general framework for convergence results to the value function is the theory of viscosity solutions. Numerical experiments are presented solving some classical pursuit-evasion games.

Keywords: Pursuit-evasion games; numerical methods; dynamic programming; Isaacs equation; Primary 65M12; Secondary 49N25; Secondary 49L20 (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2006
References: View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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DOI: 10.1142/S0219198906000886

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