a) Consider the following two-person zero-sum game:1 3 1 4 2-3 5 6120A = (-375)"Use graphical method to determine the optimal strategies for both player A and playerB and give the value of the game. b) Consider the following two-person zero-sum game:1 25A = 8 4 7-1 5 -61Using linear programming, determine optimal mixed strategies to both player and givethe value of the game.

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Answered: a) Consider the following two-person…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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5. Solve the following game for optimal strategy based on algebraic method: d=9 e: f=9 a=3 b=9 c:4 B₁ B₂ B3 9+ a 12 + b 6+c A₁ A₂ 1-d A3 6 -3 -2 14+ e 7 + f
1\2 C D 1,1 2,0 0,2 X,y A В 1. Find all possible x and y values in Real Numbers so that the strategy profile (A,C) is the dominant strategy equilibrium. 2. Find all possible x and y values in Real Numbers so that the game is a Prisoners' Dilemma.
a) Consider the following game matrix: 7 6. 9 - 4 -3 6. 10 A = 3 4 2 10 - 2 i) Determine the optimal mixed strategies. ii) Does the game have a saddle point? If so, give the value of the game and interpret it 6 ㅇ5
The following game is played by 2 players Solve the equilibrium for this game.
1 Find the set of best answers to the mixed strategy x = G33) for the game A = -1 1 1 -1
3. Consider this game in an extensive form (there are 2 players, A and B): right left B B (2, 3) (4, 2) (6, 6) (1, 9) (1, 9) (7, 7) (5, 3) a. Find the subgame-perfect equilibrium. (1) b. Explain why the players cannot reach the outcome with the payoffs circled in orange (which they both would prefer to the equilibrium outcome). (1) gauche milieu gauche milieu gauche milieu droit
2. Give an example of a 2-player, zero-sum game with the following properties (by giving its payoff matrix from the perspective of the row player): • The row player has strategy set {1, 2} and the column player has strategy set {C1, C2} • The security levels of r₁, r2, C1, and c₂ are respectively −1, −2, 4, and 3.
1. Suppose two roommates i = 1,2 must decide how much time, 5< tį < 10 (and integer), to spend on cleaning their apartment. The payoff (per unit) to roommate i = 1,2 is given by the following function: (20i Pij (50j – 30i if j 2i if j
6. Solve the following game for optimal strategy based on algebraic method: D1 D2 D3 a=8 b=7 C1 19+a | 12+b 6 c=2 d=9 C2 2 -3 -4 C3 5+d 14+a 7
b) Consider the following game matrix: -10 -2 -1 7 -5 20 -10-10 7 -1 2 7 -10 7 -1 -10 Determine optimal mixed strategies to each player and give the value of the game. -1 7 -20 -10 -1 2-10 7 -5 20 -1 -1
E/Solve the following payoff matrix to find the best strategies and the value of game: B1 B2 8 5 2 AI 1 42 3 A3 10 یا
A combo meal at Bayes' Burgers comes with fries, a burger, and a soda. The fries can be small, medium, or large, and the soda can be diet or regular. A fry cook makes the observation that 80% of the customers who choose the small fry in their combo choose a regular soda. While 60% of the customers who choose a large fry in their combo choose a diet soda. And 99% of customers who chąose the medium fry in their combo choose the regular soda. Assume 25% of customers choose a small fry in their combo, and 35% choose the large fry. If a customer chose the diet soda, what is the probability they chose the small fry?

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a) Consider the following two-person zero-sum game: 1 3 1 4 2 -5 -3 5 6 1 20 -5) A= Use graphical method to determine the optimal strategies for both player A and player B and give the value of the game.