Give an example of an extensive-form game in which player i, Game Theory

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Give an example of an extensive-form game in which player i

(a) Let i be a player with perfect recall in an extensive-form game and let σ_i be a mixed strategy of player i. Suppose that there is a strategy vector σ_-i of the other players such that ρ(x; σ_i, σ_-i) > 0 for each leaf x in the game tree. Prove that there exists a unique behavior strategy b_i equivalent to σ_i.

(b) Give an example of an extensive-form game in which player i has perfect recall and there is a mixed strategy σ_iwith more than one behavior strategy equivalent to it.

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