5. For each of the following games, identify the backwards induction equilibrium and the equilibrium strategyfor each player.a.b.2M12221R22100 101DNyd(0,2)(1,1)a(2,2)1(0,1)(1,0)a(1,1)

This question is about analyzing strategic interactions in games using the concept of backward…

Answered: 5. For each of the following games,…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

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4. Consider a normal form game with N= {1,2} and S= {A,B,C,D} x {W,X,Y,Z}. Assume that L1 allows to eliminate D and X, L2 allows to eliminate B and C, and L3 allows to eliminate Z. Provide payoffs that lead to this outcome. State the rationality assumptions explicitly.
For each of the following games, identify the backwards induction equilibrium and the equilibrium strategy for each player. 5. b. (1,1) (0,2) (2.2) (0,1) (1,) (1.0)
1. Consider the following game matrix. Player A Answer: Top Bottom Left a, b e, f Player B Right c, d g, h (a) If top and left are strictly dominant strategies, then what do we know the relationship of the parameters? (b) If (top, left) is a Nash equilibrium, then what do we know the relationship of the parameters? Answer: (c) If top and left are strictly dominant strategies, will (top, left) be a Nash equilibrium? Why? Answer: (d) If (top, left) is a Nash equilibrium, must the strategies be strictly dominant strategies? Why? Answer:
3
2
A 201.
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…
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)
The hand written is not allowed.
5. Consider a game with the following payoff table for player 1: Strategy Player 1 1 11 2 3 1 3 -4 1 Player 2 2 -3 -2 3 3 -2 −1 2 (a) Use Excel Solver to find the optimal mixed strategy for each player.

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5. For each of the following games, identify the backwards induction equilibrium and the equilibrium strategy for each player. a. b. 2 M 1 2 2 2 1 R 2 2 10 0 10 1 D N y d (0,2) (1,1) a (2,2) 1 (0,1) (1,0) a (1,1)