periods. Alice moves fifirst in period 1 and chooses x1 ∈ [0, 10]. In period 2, Bob observes Alice’s action and chooses x2 ∈ [0, 10]. The utility function of

periods. Alice moves fifirst in period 1 and chooses x1 ∈ [0, 10]. In period 2, Bob observes Alice’s action and chooses x2 ∈ [0, 10]. The utility function of player i ∈ {Alice, Bob} is ui(x1, x2) = xi(9 − x1 − x2) − xi if x1 + x2 ≤ 9 and ui(x1, x2) = −xi if x1 + x2 > 9. Find all subgame perfect equiliabria of this game. Show your work. [Note that you need to fifind strategies for each player, just listing actions on the equilibrium path is not enough.]

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