A Dijkstra-type algorithm for dynamic games
Résumé
We study zero-sum dynamic games with deterministic transitions and alternating moves of
the players. Player 1 aims at reaching a terminal set and minimising a running and nal cost. We propose
and analyse 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
di erential 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 di erential game
as the step of approximation tends to zero.
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