Identify the Nash Equilibria and Subgame Perfect Nash Equilibria in pure strategy of this game. 2. Using beliefs (p, 1−p) at P2's decision nodes in their information set, show that one of the NE is not sequentially rational.
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1. Identify the Nash Equilibria and Subgame Perfect Nash Equilibria in pure strategy of this game.
2. Using beliefs (p, 1−p) at P2's decision nodes in their information set, show that one of the NE is not sequentially rational.
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- a. Consider the following sequential game. Player 1 A B Player 2 Player 1 a a B Player 2 (4) () y i. Determine the subgame perfect Nash equilibria and their outcomes. ii. Determine the Nash equilibria of the game. For each of the Nash equilibria, argue why no player has a profitable deviation. ii. Determine which parts of the Nash equilibrium strategies involve uncredible threats.1. Nash Equilibrium (a) Find all pure Nash Equilibria P1/P2 W X Y Z 9,9 0,7 5,5 1,1 7,0 0,0 4,2 7,7 5,5 2,4 0,0 1,1 1,1 7,7 1,1 0,0 A B C D (b) Consider the following picnic game. There are N players in the game each who can chose to bring food to the picnic or not. Let b;= {0, 1} be player i's choice of bringing food with 0 as not and 1 as yes. If they decide to bring food it comes at a cost c;(1) = 1 and no cost to bring food. Payoffs are sum of food brought minus individual cost. i. Write out the normal form matrix if N = 2 ii. If N = 2 find all pure Nash Equilibria iii. Find all pure Nash Equilibria in the general gameし(5,3) b I(2,2) も(0,0) (4,12) a (12.4) (0,0) i). List all subgame pertect Nash equilibria and name one Nash eqvilibrivm that is not subgame pertect i). How many strategies does playot and player 2 have?
- • Japan's Elpida Memory entered court management and was acquired by Micron. The media reported that it was the result of the semiconductor chicken game. • Question (a) Where is the Nash Equilibrium? • Question (b) What is the mixed-strategy equilibrium? • Question (c) What is the probability of a chicken game? Elpida Quantity Maintain Quantity Increase (1-y) Quantity Maintain (x) 10, 1 9, 2 Samsung Quantity Increase (1-x) 12, -1 7, -1.4 operating profit (trillion won)1. Consider the following normal form game. X Y (a) What is the set of rationalizable strategies for this game? Player 1 Player 2 W Q 1,7 1,5 2,3 Z 3,4 0,4 0,6 R= (b) The game has only one Nash equilibrium and it is a mixed strategy Nash equilibrium. Compute and report this equilibrium. Equil. strategy profile:Consider the game with the payoffs below. Which of the possible outcomes are MORE efficient than the Nash Equilibrium (NE)? Note, they do NOT need to be Nash equilibria themselves, they just need to be more efficient than the NE. Multiple answers are possible, but not necessary. You need to check ALL correct answers for full credit. JILL High Medium LowMAGGIE Left 3,4 2,3 2,2Center 4,8 9,7 8,7Right 7,6 8,5 9,4Group of answer choices (Left, Low) There is no strategy combination that is more efficient than the Nash equilibrium for this game. (Right, Medium) (Left, High) (Center, Medium) (Center, High) (Center, Low) (Left, Medium) (Right, Low) (Right, High)
- i. ii. QUESTION ONE A. A Nash equilibrium is a strategy profile such that every player's strategy is the best response to all the other players. It requires that each player makes a best response and that expectations regarding the play of other players are correct. Below is the table showing strategies and payoff for Player 1 and Player 2. PLAYER 1 R1 R2 R3 R4 C1 0,7 5,2 7,0 6,6 C2 2,5 3,3 2,5 2,2 PLAYER 2 C3 7,0 5,2 0,7 4,4 CA 6,6 2,2 4,4 10,4 REQUIRED; Transform the normal form game above into an imperfect extensive game form Find the Nash equilibrium for the game above using iterative deletion of strictly dominated strategies. Find the Nash equilibrium using brute force or cell by cell inspection.1. Assume this game is played 2 times and there is no discounting. The whole payoff for two periods is the sum of payoffs of each period. Draw a tree of the game and solve it with subgame prefect Nash equilibrium. Explain clearly, handwritten is preferable.Consider the following game. Which one of the following statements is FALSE? 1. There are 7 subgames in this extensive-form game. 2. There are 6 proper subgames in this extensive-form game. 3. (BK, CE) is a Subgame Perfect Nash Equilibrium. 4. (BK, DE) is a Subgame Perfect Nash Equilibrium
- Which is the correct mixed strategy Nash equilibrium for the below game? A B Confess Confess (3,2) Doesn't (0,0) confess a. (2/5); (3/5) b. (1/4); (3/4) c. (1/2); (1/2) d. (1/3); (2/3) Doesn't confess (0,0) (2,3)Subgames • • • At each node where a player makes a decision, we can think about the "subgame" starting at that node A subgame is the portion of the tree following a particular node How many subgames does our first sequential move example have? • How many subgames does our entry game have? • How many subgames does the game on the right have? • What are its Nash equilibria? Player 1 (1,4) T Player 2 U B (5,2) (3,3) р Player 1 D L 9 (2, 0) Player 2 R (6, 2)In a game, a Nash equilibrium is reached only if the players ________. a. understand the game and the payoffs associated with each strategy b. use backward induction to develop their strategies c. follow a mixed strategy d. have no best response for the choices made by other players