Stackelberg博弈课件.pdf

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MS&E 246: Lecture 7 Stackelberg games Ramesh Johari

Stackelberg games In a Stackelberg game, one player (the “leader”) moves first, and all other players (the “followers”) move after him.

Stackelberg competition • Two firms (N = 2) • Each firm chooses a quantity sn ≥ 0 • Cost of producing sn : cn sn • Demand curve: Price = P(s1 + s2) = a – b (s1 + s2) • Payoffs: Profit = Πn(s1, s2) = P(s1 + s2) sn – cn sn

Stackelberg competition In Stackelberg competition, firm 1 moves before firm 2. Firm 2 observes firm 1’s quantity choice s1, then chooses s2.

Stackelberg competition We solve the game using backward induction. Start with second stage: Given s1, firm 2 chooses s2 as Π2(s1, s2) s2 = arg maxs2 ∈ S2 But this is just the best response R2(s1)!

Best response for firm 2 Recall the best response given s1: Differentiate and solve: So:

Firm 1’s decision Backward induction: Maximize firm 1’s decision, accounting for firm 2’s response at stage 2. Thus firm 1 chooses s1 as s1 = arg maxs1 ∈ S1 Π1(s1, R2(s1))

Firm 1’s decision Define tn = (a - cn)/b. If s1 ≤ t2, then payoff to firm 1 is: If s1 > t2, then payoff to firm 1 is:

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