An information set of a player with perfect recall

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Let U and U^ be two information sets (they may both be the information sets of the same player, or of two different players). U will be said to precede U^ if there exist a vertex x ∈ U and a vertex x^ ∈ U^ such that the path from the root to x^ passes through x.

a) Prove that if U is an information set of a player with perfect recall, then U does not precede U.

(b) Prove that in a two-player game without chance moves, where both players have perfect recall, if U precedes U^, then U^ does not precede U.

(c) Find a two-player game with chance moves, where both players have perfect recall and there exist two information sets U and U^ such that U precedes U^, and U^ precedes U.

(d) Find a three-player game without chance moves, where all the players have perfect recall and there exist two information sets U and U^ such that U precedes U^, and U^ precedes U.

Reference no: EM131332306

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