THE PEDESTRIAN PRINCIPLE FOR DIFFERENTIAL GAMES

Richard H. Stockbridge () and Ziyu Zheng ()
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Richard H. Stockbridge: Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI 53201-0413, USA
Ziyu Zheng: Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI 53201-0413, USA

International Game Theory Review (IGTR), 2006, vol. 08, issue 04, 715-737

Abstract: A dynamic normal formulation for differential games is introduced and the "pedestrian principle" is discussed as a means of dynamically implementing the equilibrium strategy in a single game. Our formulation emphasizes the distinction between a player's rational prediction and the actual evolution of the game dynamics. To model the free will of players, a randomized strategy is introduced which serves as the justification of mixed strategies and the bridge from a static analysis to a dynamic one. Existence of Nash equilibrium in the class of mixed strategies is proved for non-cooperative deterministic differential games.

Keywords: Differential game; dynamic; equilibrium; mixed strategy; Nash equilibrium; non-cooperative; stopping game; pedestrian principle; randomized strategy; rational; stochastic; 91A; 60H (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1142/S0219198906001211

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