Consider the below matrix game:P2LM20RU 8,10,24,0P1 C3,31,20,0D 5,02,38,1Assume P₁ has belief 0-1 = (0-1(L), 0-1(M), 0-1(R)) = 3, x) and plays strategy σ₁ =(0₁(U), 0₁(C), 0₁(D)) = (³, y,³).a) What is P₁'s belief over the strategy that P2 will play? (What is x?)

Step 1: The question asks for the value of x in the belief of player 1 over the strategy that player…

Answered: Consider the below matrix game: P2 L M…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question 22 Consider the following Extended Form Game: 01 02 04 A O 3 (2,3) P1 A' (5,5) A' (3,8) B A P2 B' P2 B' (1,9) According to backwards-induction, in how many steps does the game end? P1 B (9,1)
10
Please select the correct option and write clear. Thank you.
5) The following is a matrix represantation of a simultaneously played game. Alice/Bob Film Ball Game 4,2 0,0 0,0 1,3 a) Draw players' best response functions agains each other Film Ball Game
Consider the payoff matrix listed below: IS |1, -1 3, 0 |2, 1 0, 3 1, 2 |0, 0 3, 1 5, 3 2, 1 What is the Nash Equilibium of the game? a. (B, R) b. (U, Q) c. (B, S) d. (C, Q) M/2/6
1. Consider a sequential continuum game with two players, in which Player 1 first chooses a continuous variable £₁, and then Player 2 selects £2, with payoff functions ₁ and 7₂. Find the best response for P2, as the function î2 = BR₂(x1), for each given #₂: (a) (b) (c) T₂(x1, x₂) ) = (1400 — x1 — x2)x2 − 13x² T₂(x1, x₂) T₂(X1, X2₂) = : 100x2 + 3x1x2 − 14x1 – 30x1x² = 15x2 x² + x² +1
Consider the following two-player game with three options for each player. (Payouts are listed for the row player first, then the column player.) player Y layery 3,3 A 1,5 4,4 6,2 K 8,1 3,7 5,2 0,6 1,1 Find a mixed Nash equilibrium for this game. Solution suggestion: Use two variables per player. If p and are the probabilities of selecting the first two strategies, then 1-p-q is the probability of selecting the third strategy. You will need to solve a system of equations.
Please try to solve it in 30 minute
2) Two firms, X and Y, are planning to market their new products. Each firm can develop either TV or Laptop. Market research indicates that the resulting profits to each firm for the alternative strategies are given by the following payoff matrix: FIRM Y TV LAPTOP FIRM X TV 30, 30 60, 35 LAPTOP 40,70 20, 20 A) If both firms make their decisions at the same time and follow maximin (low-risk) strategies, what will the outcome be? B) Suppose both firms try to maximize profits, but Firm X has a head start in planning, and can commit first. Now what will the outcome be? What will the outcome be if Firm Y has a head start in planning and can commit first? C) What is the cooperative outcome? D) Which firm benefits most from the cooperative outcome? How much would that firm need to offer the other?
Problem 4: Consider an infinitely repeated game, where the base game is the following 2-person 2x2 game: A A 0,0 10, 10 S1: choose A always S2: choose B always B 10, 10 0,0 Assume both players discount the future at the same rate of r, 0 < r < 1. Limiting each player's strategies to the following six possibilities, S3: Choose A then mimic the other player's previous choice S4: Choose B, then mimic the other player's previous choice S5: Choose A, then choose the opposite of the other player's previous choice S6: Choose B, then choose the opposite of the other player's previous choice a. present the strategic form of this game, b. identify all pure-strategy Nash equilibria c. does repetition with these strategies "solve" the coordination dilemma that confronts the players in the single play of the above game.
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Consider the below matrix game: P2 L M 20 R U 8,1 0,2 4,0 P1 C 3,3 1,2 0,0 D 5,0 2,3 8,1 Assume P₁ has belief 0-1 = (0-1(L), 0-1(M), 0-1(R)) = 3, x) and plays strategy σ₁ = (0₁(U), 0₁(C), 0₁(D)) = (³, y,³). a) What is P₁'s belief over the strategy that P2 will play? (What is x?)