Necessary conditions of parametric extremum for nash equilibrium in mixed strategies in differential games

1992 ◽  
Vol 3 (4) ◽  
pp. 414-416
Author(s):  
�. R. Smol'yakov
Keyword(s):  
Nash Equilibrium ◽  
Differential Games ◽  
Necessary Conditions ◽  
Mixed Strategies

THE PEDESTRIAN PRINCIPLE FOR DIFFERENTIAL GAMES

2006 ◽  
Vol 08 (04) ◽  
pp. 715-737
Author(s):  
RICHARD H. STOCKBRIDGE ◽  
ZIYU ZHENG
Keyword(s):  
Nash Equilibrium ◽  
Free Will ◽  
Differential Games ◽  
Static Analysis ◽  
Equilibrium Strategy ◽  
Mixed Strategies ◽  
Game Dynamics

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.

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