HEAD and Dunlop set prices simultaneously for their respective tennis rackets. Let p₁ ≥ 0denote the price set by HEAD and p2 ≥ 0 the price set by Dunlop. Consumers demand4-2p1+p2 billions of HEAD rackets and 4-2p2+p₁ billions of Dunlops's. Assume that thecost of producing a tennis rackets is 0, so the payoff of HEAD is v₁ (P₁, P2) = P1(4-2p₁+P2),and the payoff of Dunlop is v2 (P1, P2) = P2(4-2p2 +P₁).(a)What is the best-response p₁ = BR₁(p2) of HEAD to a price p2 chosen byWhat is the best-response p2 = . BR₂ (p1) of Dunlop to a price p₁ chosen byDunlop?HEAD?Find the Nash equilibrium of this game.Which strategies are rationalizable (i.e., survive the process of iteratedof strategies that are not best responses for any surviving play of theeliminatioopponent,.(d)Suppose both firms choose prices p = P2 = 2. Does this outcome Paretodominate the Nash equilibrium?(b)(c)

The best response in economics or game theory is the strategy (or strategies) that generates the…

HEAD and Dunlop set prices simultaneously for their respective tennis rackets. Let p₁ ≥ 0 denote the price set by HEAD and p220 the price set by Dunlop. Consumers demand 4-2p1+p2 billions of HEAD rackets and 4-2p2+P₁ billions of Dunlops's. Assume that the cost of producing a tennis rackets is 0, so the payoff of HEAD is v₁ (P1, P2) = P₁(4-2p₁+P₂), and the payoff of Dunlop is v2 (P1, P2) = P2(4-2p2+P1). (a) What is the best-response p₁ = BR1(p2) of HEAD to a price p2 chosen by What is the best-response p2 = BR₂(p1) of Dunlop to a price p₁ chosen by Dunlop? HEAD? Find the Nash equilibrium of game (b)

HEAD and Dunlop set prices simultaneously for their respective tennis rackets. Let p₁ ≥ 0 denote the price set by HEAD and p220 the price set by Dunlop. Consumers demand 4-2p1+p2 billions of HEAD rackets and 4-2p2+P₁ billions of Dunlops's. Assume that the cost of producing a tennis rackets is 0, so the payoff of HEAD is v₁ (P1, P2) = P₁(4-2p₁+P₂), and the payoff of Dunlop is v2 (P1, P2) = P2(4-2p2+P1). (a) What is the best-response p₁ = BR1(p2) of HEAD to a price p2 chosen by What is the best-response p2 = BR₂(p1) of Dunlop to a price p₁ chosen by Dunlop? HEAD? Find the Nash equilibrium of game (b)

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter15: Imperfect Competition

Section: Chapter Questions

Problem 15.12P

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