12Extensive Forms

# 12Extensive Forms - Extensive Form Games Revised item 7 An...

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Extensive Form Games Revised item 7 An extensive form game is a collection Γ = ( N,A,H,T,ι, I , ( U i ) i N ). 1. N , a ﬁnite set of players . 2. A , a (ﬁnite) set of actions . 3. H , a (ﬁnite) set of histories (sometimes called nodes), with (a) h 0 H , where h 0 is the empty history . (b) h H -{ h 0 } only if h = h 0 ,a 1 ,...,a k for some integer k 1 where a A for = 1 ,...,k . (c) For any k 2, if h = h 0 ,a 1 ,...,a k H , then h = h 0 ,a 1 ,...,a k - 1 H . 4. A ( h ) = { a A | ( h,a ) H } is the set of actions available at h H . 5. T = { h H | ( h,a ) / H for any a A } . T is the set of terminal histories (or outcomes ). 6. A function ι : H \ T N which indicates which player has the move at each non-terminal history. 7. A partition I of H \ T such that for any two members h,h 0 of the same partition element (i) A ( h ) = A ( h 0 ); (ii) ι ( h ) = ι ( h 0 ). Each element of I is an information set . For any h H \ T , let I
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