4. The following payoff matrix shows the profit payoff to firms A and B from combinations of price strategies HI and LO. A B HI HI (6,6) LOW (16,-5) LOW (-7, 15) (0, 0) (a) In a one period game, what strategy would each firm follow, and why? Determine the equilibrium on the one-period game. (b) Now assume the game is infinite in length. Firm B goes HI in period 1 and continues with HI so long as A does as well. Firm A is deciding between HI and LO. Determine the range of discount rates for which HI is the better choice for Firm A.

4. The following payoff matrix shows the profit payoff to firms A and B from combinations of price strategies HI and LO. A B HI HI (6,6) LOW (16,-5) LOW (-7, 15) (0, 0) (a) In a one period game, what strategy would each firm follow, and why? Determine the equilibrium on the one-period game. (b) Now assume the game is infinite in length. Firm B goes HI in period 1 and continues with HI so long as A does as well. Firm A is deciding between HI and LO. Determine the range of discount rates for which HI is the better choice for Firm A.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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3. Consider a two-stage game of R&D competition. The players are firm i and j, each produces with different marginal cost c₁ and cj, where i, j = 1, 2 and i ‡ j. The rules are the firms first invest, denoted by I, and I,, in cost-reducing innovation, they then engage in Cournot competition in the output market by deciding qk, k = i, j and i j simultaneously. The payoffs to the firms are their profits. (a) write out the objective function for firm i and j at the R&D stage and that at the output stage. (b) Assuming that p'(Q) 0 and 1 p"Q+3p' (c) dvi dli < 0. C əqi aci - p"qj+2pi p'(p"Q+3p') даі acj = p"qi+p' p' (p"Q+3p') aQ aci - show, in the R&D stage, that the first-order conditions are = [p' (Q (C₁, c₁)) a daj(crcj) — 1] qi (C₁, Cj) = qp² (Ii, 1, č¡, ēj) = 0. And aci Ij=constant (d) In a closed economy, show that the total differentiation of the national welfare function is dw = −p' (qidqi+q;dqj) — q₁dc₁ — q¡dc; – dl; – dlj. - -
Which of the following accurately describes a player's strictly dominant strategy? O It is a strategy that is better than all the player's other strategies, no matter what the other players do. There is always at least one player who has one in every game.. O It is the strategy a player uses in the Nash equilibrium of a game. Since a Nash equilibrium always exists, players always have a strictly dominant strategy. O It is a strategy that is better than all the player's other strategies, no matter what the other players do. A player may or may not have one. O It is a strategy that is better than all the player's other strategies, no matter what the other players do. Every player has a dominant strategy in every game.. O It is the strategy a player uses in the Nash equilibrium of a game. Since a Nash equilibrium may not exist, players may not always have a strictly dominant strategy.
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Little Kona is a small coffee company that is considering entering a market dominated by Big Brew. Each company's profit depends on whether Little Kona enters and whether Big Brew sets a high price or a low price: Little Kona True True or False: Only Little Kona has a dominant strategy in this game. False Big Brew High Price Low Price Enter $2 million, $3 million $2 million, $1 million Don't Enter 50, 58 million $0, $3 million Which of the following outcomes represent a Nash equilibrium in this case? Check all that apply. Big Brew maintains a high price and Little Kona does not enter. Big Brew maintains a low price and Little Kona does not enter. Big Brew maintains a high price and Little Kona enters. Big Brew maintains a low price and Little Kona enters. Big Brew threatens Little Kona by saying, "If you enter, we're going to set a low price, so you had better stay out." Thin True or False: Little Kona should believe the threat.
Wal-Mart's dominant strategy is to pick a price of $. Target Price = $30 Price = $17 %3D What is the Nash equilibrium for this game? $6,000 $1,500 O A. The Nash equilibrium is for Target to choose a price of $17 and Wal-Mart to choose a price of $30. Price = $30 $6,000 $11,000 O B. The Nash equilibrium is for Target and Wal-Mart to both choose a price of $30. Wal - Mart C. The Nash equilibrium is for Target to choose a price of $30 and Wal-Mart to choose a price of $17. $11,000 $4,500 Price = $17 %3D $1,500 $4,500 O D. The Nash equilibrium is for Target and Wal-Mart to both choose a price of $17. South OE. O E. A Nash equilibrium does not exist for this game.
2. Consider an infinitely repeated game in which, in each period, two firms with zero costs choose quantities and prices are given by: p1 = 1 - q1 - q2/2, p2 = 1 - q2 - q1/2. Firms have a common discount factor of 8 = 1/2. a) Explain what a trigger strategy is and determine whether the firms can attain the joint profit maximising outcome in a subgame perfect equilibrium using trigger strategies. b) Explain what a stick and carrot strategy is and discuss whether it is possible to attain the joint-profit maximising outcome in a subgame perfect equilibrium using stick and carrot strategies.
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A 201.
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3. Consider the following game: K Out 2 2 1 9 Player 1 Player 1 X In A Y Player 2 0 2 B 5 5 a) Does the game have perfect information? Why/why not? b) Circle the subgames. c) Find all backward induction solutions. d) Below are written five strategy profiles. One of them is a subgame perfect equilibrium; circle it! One of them is not a Nash equilibrium; write "X" across it! ((Out, X), A) ((Out, Y), A) ((In, Y),B) ((Out, Y), B) ((In, X),B)