1. (Dynamic Game with Perfect Information) Consider the following three playergame of perfect information depicted belowPlayer 1Player 3h"RPlayer 2abPlayer 3Player 32-10Sh22h.13504Identify all pure strategy Nash Equilibria for the game. Verify which purestrategies are also subgame perfect equilibria

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Answered: 1. (Dynamic Game with Perfect…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

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4.Find the Nash equilibrium of the game in table,and explain it . Player 2 迪夫 L 5802E110 U 2, -2 -2, 2 M -2, 2 2, -2 Player 1
11. What are the subgame perfect equilibria of the following game? Out In T B 7,21 L R L/R 9,3 1,1 1,1 3,9 (a) (InT, L), (OutB, R) and (OutT+OutB, L + R). (b) (InT, L) and (OutB, R). (c) Out and (InT, L). (d) (InT, L), (OutB, R) and (OutT+OutB, L + R). (e) (InT, L). 2
4. Game theory terminology Select the term that best describes each definition listed in the following table. Prisoners' Payoff Matrix Nash Dominant Tit-for-tat Dilemma Definition Equilibrium Strategy Collusion Strategy Game A set of strategies (one for each player) in which each player's strategy is the best option for that player, given the chosen strategy of the player's opponents The event that occurs when agents in a game form an agreement about which strategies to implement A player's best choice, if it exists, regardless of his or her opponent's strategy A strategy in which a player cooperates until the other player defects and then defects until the other player cooperates again
60B- What is the Nash equilibrium for this game and identify the profit each player gets at this solution 5 m
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:
UofC Aggressive Restrained Aggressive 18, 26 29,47 MRU Restrained 45, 59 32, 23 Consider the case of a Sequential-Move game. Uofc moves First Part 1. Is UofC 's sub-game Perfect Nash Equilibrium strategy Aggressive or Restrained? (Answer 1 for aggressive and 2 for Restrained) 1 Part 2. Is MRU's sub-game Perfect Nash Equilibrium strategy Aggressive or Restrained? (Answer 1 for aggressive and 2 for Restrained) Number: Part 3. How much profit does UofC make under the Sub-game perfect Nash-Equilibrium? Number Part 4. How much profit does MRU make under the Sub-game perfect Nash-Equilibrium? Number
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…
Question 28 Suppose the following game: I Player 1 nice nice Player 2 50, 50 mean 90,20 Which of the following is true? mean 20,90 30, 30 O Both players play "mean" with a 70 % chance, and "nice" with a 30% chance. O There is no Nash Equilibrium in pure strategies, there is only one Nash Equilibrium in mixed strategies. Both players play "nice" with a 70% chance, and "mean" with a 30% chance. There is no Nash Equilibrium in mixed strategies, there is only one Nash Equilibrium in pure strategies.
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)
FOOP 6. (a) For the following extensive-form game: i. Identify the pure and mixed strategy Nash Equilibria. ii. Is the set of pure and mixed strategy Subgame Perfect Nash equilibria of the game different from the set of equilibria identified in part (a)? Explain (a couple of sentences should suffice). (3,1) A D B C (-2,-2) (2,5) D (0,7)

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