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Show the number of subgames on the game threes below
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- Consider the following representation of a Normal form game. actions w a (45,22) (10,38) (42,13) (10,7) (p,28) (15,40) (q,10) (44,10) (20,22) (14,31) (27,13) (12,8) d. (20,41) (9,48) (28,24) (18,32) Here each cell in the table represents an ordered pair. First element is payoff of the first player and second element is payoff of the second player. The letters a, b, c, d, x, y, z, w represent the actions. Write down the table in your answer script too. Now answer the following questions: 1. What is the distinction between strictly dominant strategy and weakly dominant strategy? Is it reasonable for a player to play a strictly dominated strategy? Explain why. 2. What are the minimum values for p and q that will make ba strategy that strictly dominates all other strategies for player 1, assuming both p and q are natural numbers? 3. Does player 2 have any strictly dominated pure strategy? If yes, which pure strategy dominates that strategy? If the submit button is off it is beacuse the due…6. Battle of the Networks 1\2 %share Sitcom Sitcom 48;52 Sport 42;58 Nature 55:45 58;42 Ans: s; = (0; 0.85; 0.14); V, = 55.43 s; = (0.43; 0.57;0); V½ = 44.57 40;60 63;37 60;40 Sport Nature 56:44 52;48 Find Nash Equilibrium.Let G₁, G₂ and G3 be the following games. Colin A B Rose A (10,3) (7.5) B (6,6) (8,4) G₁ Rose Rose Colin A Colin A B A (5,8) (4.2) B (9.2) (3,5) G₂ B (3,6) A (4,4) B (5.3) (2,7) G3 Rose and Colin play the following dynamic game with Rose moving first. In her first move, Rose has a choice of either 0 or 3. If she chooses 3, then Rose and Colin play G3 with Colin moving first. If Rose chooses 0 in her first move, then Colin can play either 1 or 2 in his first move. If he plays 1, then Rose and Colin play G₁ with Rose moving first, and if he plays 2, then Rose and Colin play G₂ with Rose moving first. Draw the game tree associated with this game, and find the backwards induction solution.
- Let G₁, G₂ and G3 be the following games. Colin A Rose B A (10,3) (7,5) B (6,6) (8.4) G₁ Rose Rose Colin A B A (4,4) (3,6) B (5,3) (2,7) G3 Colin A B A (5,8) (4,2) B (9,2) (3,5) G₂ Rose and Colin play the following dynamic game with Rose moving first. In her first move, Rose has a choice of either 0 or 3. If she chooses 3, then Rose and Colin play G3 with Colin moving first. If Rose chooses 0 in her first move, then Colin can play either 1 or 2 in his first move. If he plays 1, then Rose and Colin play G₁ with Rose moving first, and if he plays 2, then Rose and Colin play G₂ with Rose moving first. Draw the game tree associated with this game, and find the backwards induction solution.Consider the following game: Player 1 T M B N R (1,2) (1,1) (3,4) (1,-1) L Player 2 (-1,2) (2, -1) (0,1) (4,4) S (3,2) (4,5) (5,4)) (6,1) Q (1,5) (1,2) (4,1) (1,4) a) Does player 1 (the row player) have any dominated strategies. If yes, list all such strategies b) Find all the Pareto Optimal strategy profiles in the game. c) Let 0= (1/2, 0,1/4,1/4). Find BR₂(0).Exercise 6.1Suppose that two airlines decide to collude. Analyse the game between these two companies. Suppose that each of them can charge for tickets a high price or a low price. If one of them charges 100 euros, it gets few profits if the other also charges 100 euros and high profits if the other charges 200 euros. On the other hand, if the company charges 200 euros, it obtains very little profit if the other charges 100 euros and an average profit if the other also charges 200 euros. a) Represent the matrix of results of this game. b) What is the Nash equilibrium in this game? Explain your answer. c) Is there an outcome that would be better than the Nash equilibrium for the two airlines? How could it be achieved? Who would lose out if it were reached?
- Find the perfect Bayesian equilibria in the following two-person game: B. Chance 1/4 U 3/4 2 L \R (:) (?) (3) (6) () (:) (:) (*) 8AsapGame Theory Question A non-profit firm is on a local community online donation platform for a community event it wants to hold (only community members can donate via the website). The event will be held only if the non-profit firm collects $20,000 total from members of the community. Each member values the event at $500. Suppose that there are 100 community members. Community members can only donate by purchasing a lottery ticket from the firm. Each ticket costs $200 and only one ticket can be purchased per member. The proceeds will be collected by the firm. The lottery winner gets a premier meal at a local restaurant that's worth $100. Remember, the firm keeps all the donated money. If the amount of donations is less than $20,000, then the firm returns the donated money to the community members (since there'll be no event held but the lottery winner still gets to eat that fancy meal). If the donations sum up to $20,000, the community event will take place. What are the Nash…
- Y A BA B (PERFECT-INFO GAME) Consider the game shown at the right. -1 a. What is the number of pure strategies of Player 1? Player 2? 2 -2 4 b. How many subgames are in this game? c. Find all subgame perfect equilibria (SPE)? -2 d. Find all other NE which is not SPE. -3(a) Stan and Ollie are two students who share a flat. Both of them prefer to live in a clean flat. However, neither is too fond of housecleaning. Each of them receives a payoff of 12 if they both clean the flat. If neither person cleans the flat, they receive a payoff of 6 each. If one person cleans the flat but the other person does not, then the payoff for the person who does the cleaning is 5 and the payoff for the person who doesn't do any cleaning is 15. (i) Write down the payoff matrix of this game. Derive the dominant strategy equilibrium. Is this also a Nash equilibrium? (ii) Expiain your reasoning. Consider a game with N players. Each player chooses Black or White. If a player (b) chooses Black, she gets 100 if everyone else also chooses Black, and she gets 0 if any of the other players does not choose Black. If a player chooses White, she always gets 50. Show that everyone choosing Black and everyone choosing White are both Nash equilibria of this game.Consider the Normal Form Game characterized in the following figure: P1 \ P2 A1 A2 A3 A4 B1 B2 B3 B4 (-1,1) (0,0) (1,-1) (2,0) (-2,-2) (2,7) (-1,-1) (-1,1) (5,7) (3,5) (0,0) (0,8) (0,3) (-1,-1) (10,2) (0,0) Which is the set of rationalizable actions? O (A2, A4)x(B2, B3) O (A1, A2)x(B1, B2, B4) O (A1, A3)x(B1, B4) O (A1, A3, A4}x{B1, B3)