0 logging firms use a forest to collect timber. Each firm i must choose how many trees to cut, g, The benefit of cutting a ree is 1000-2G per tree, where G is the total quantity of trees cut in the forest. The marginal cost of cutting a tree is 10G. Firms do not face any fixed costs. In a Nash Equilibrium, O Each firm cuts 125 trees O Each firm cuts 125/10 trees O Each firm cuts 125/4 trees Each firm cuts 5 trees

0 logging firms use a forest to collect timber. Each firm i must choose how many trees to cut, g, The benefit of cutting a ree is 1000-2G per tree, where G is the total quantity of trees cut in the forest. The marginal cost of cutting a tree is 10G. Firms do not face any fixed costs. In a Nash Equilibrium, O Each firm cuts 125 trees O Each firm cuts 125/10 trees O Each firm cuts 125/4 trees Each firm cuts 5 trees

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Q² 4 PROBLEM (4) Firm A and Firm B with identical total costs TCA (QA) related goods and competing in prices (Bertrand competition), with demands: QA = 510 - 2PA + pв and Qв= 510 - 2pв+ pa, respectively. = and TCB (QB) Q² 4 are producing (a) Calculate the Bertrand-Nash equilibrium prices. (b) Calculate the prices they charge when A is the leader and sets its price first, anticipating B's best response and taking it into account (like in Stackelberg competition). (c) Calculate the prices they charge when they collude, in order to maximize sum of their profits.
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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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2. For the game illustrated in the figure below, find all pure-strategy Nash equilibria and mixed- strategy Nash equilibria (Hint: apply IDSDS first) Player 2 W y 0,20 А 5,30 10,15 Player 1 В 0,5 15,5 5,10 0,5 0,30 -10,5
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Consider the game R T 11 1.0 10 M 014.0 0.1 B 0.10. 4.0 (a) Find the Nash equilibrium in pure strategies. (b) Find the Nash equilibrium in completely mixed strategies. (c) Find the Nash equilibrium in partially mixed strategies ove the support {A. B} x {C.R).
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1. Static and Dynamic Game. Consider the following 2-by-2 game: C D 1A (1,10) (1,1) B (2, a) (0,1) (a) erwise, find the pure-strategy Nash equilibria, if any of this game. (There is no need to look for equilibria in mixed strategies) Assume for now that a = 2. Using dominant strategies or oth- (b) Now, consider the dynamic game in which player 1 moves before player 2, and the payoffs remain unchanged. i.: possible strategies for each player? Recall that a strategy profile for a player not at the initial node of the game tree must specify an action for the player at every node. Draw the game tree for this dynamic game. What are the ii "Find the backward-induction solution(s) to this game. Calculate the equilibrium payoffs for each player. Com- pared to the simultaneous game, is there a first-mover advantage or a ii. second-mover advantage? (c) Now, assume that a = 0 in the original static game. i. Find all the Nash equilibria in pure and mixed strategies. Denoting p the probability…