普林斯顿大学博弈论讲义10(3)

普林斯顿大学博弈论讲义3-10

3,3r 12,2d 1a 1

r 2D A 1,1r 1d 2a 20,0

Figure 1:A perfect-information game

Strategies and normal form(s)

De?nition 1is arguably a “natural”way of describing a dynamic game—and one that is at least implicit in most applications of the theory.

According to our formulations,actions are the primitive objects of choice.However,the notion of a strategy ,i.e.a history-contingent plan,is also relevant:

De?nition 2Fix an extensive-form game with perfect information Γ.For every history h ∈X ,let A (h )={a ∈A :(h,a )∈H }be the set of actions available at h .Then,for every player i ∈N ,a strategy is a function s i :P ?1(i )→A such that,for every h such that P (h )=i ,s i (h )∈A (h ).Denote by S i and S the set of strategies of Player i and the set of all strategy pro?les.

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