普林斯顿大学博弈论讲义10(4)

Armed with this de?nition (to which we shall need to return momentarily)we are ready to extend the notion of Nash equilibrium to extensive games.

De?nition 3Fix an extensive-form game Γwith perfect information.The outcome function O is a map O :S →Z de?ned by

?h =(a 1,...,a k )∈Z, <k :a +1=s P ((a 1,...,a ))((a 1,...,a ))

The normal form of the game Γis G Γ=(N,(S i ,u i )i ∈N ),where u i (s )=U i (O (s )).

The outcome function simply traces out the history generated by a strategy pro?le.The normal-form payo?function u i is then derived from U i and O in the natural way.Finally:De?nition 4Fix an extensive-form game Γwith perfect information.A pure-strategy Nash equilibrium of Γis a pro?le of strategies s ∈S which constitutes a Nash equilibrium of its normal form G Γ;a mixed-strategy Nash equilibrium of Γis a Nash equilibrium of the mixed extension of G Γ.

3

搜索“diyifanwen.net”或“第一范文网”即可找到本站免费阅读全部范文。收藏本站方便下次阅读，第一范文网，提供最新教学研究普林斯顿大学博弈论讲义10(4)全文阅读和word下载服务。