Consider the game "Battle of the Sexes" as below. In the mixed-strategy equilibrium, Michelle chooses to watch a movie with the probability y" of: Michelle Watch soccer Watch a movie Roger Watch soccer 2,1 0,0 Watch a movie 0,0 1,2 O 0.5 O 1/3 O 2/3 O 2/5
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- O Macmillan Learning In this game table, the Nash equilibrium is Mario's Fancy Mario's Casual Isabella's Fancy Isabella's Casual 3,6 4,8 O Casual, Fancy = (4,8) O Fancy, Casual = (7, 2) O Casual, Casual = (9, 7) O Fancy, Fancy = (3,6) 7,2 9,76. 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.Game 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…
- $11. Anne and Bruce would like to rent a movie, but they can't decide what kind of movie to get: Anne wants to rent a comedy, and Bruce wants to watch a drama. They decide to choose randomly by playing "Evens or Odds." On the count of three, each of them shows one or two fingers. If the sum is even, Anne wins and they rent the comedy; if the sum is odd, Bruce wins and they rent the drama. Each of them earns a payoff of 1 for winning and 0 for losing "Evens or Odds." (a) Draw the game table for "Evens or Odds." (b) Demonstrate that this game has no Nash equilibrium in pure strategies.Exercise 6.8. Consider the following extensive-form game with cardinal payoffs: 1 R O player pay 000 2 1 M 3 b 010 O player 3's payoff 1 2 221 2 000 0 0 (a) Find all the pure-strategy Nash equilibria. Which ones are also subgame perfect? (b) [This is a more challenging question] Prove that there is no mixed-strategy Nash equilibrium where Player 1 plays Mwith probability strictly between 0 and 1.Consider the following simultaneous move game: Player 1 U M D Player 2 L 2,10 2,5 8,7 C 5,2 11,8 8,4 R 5,4 2,9 8,3 In the Nash equilibrium of this game, player 1 receives a payoff of ✓ and player 2 receives a payoff of
- Consider the game of Chicken in which each player has the option to “get out of the way” and “hang tough” with payoffs: Get out of the way Hang tough Get out of the way 2,2 1,3 Hang tough 3,1 00 a. Find all pure strategy Nash equilibria, if they exist b. Let k be the probability that player 1 chooses “hang tough” and u be the probability that player two chooses “hang tough.” Find the mixed stragety Nash equilibria, if they existQuestion 4. Zeynep and Mehmet will eventually play the following game. Mehmet L R U 3,1 0,0 Zeynep D 0,3 1,3 In a preliminary stage, Zeynep has already asked Mehmet to allow her to move first and proposed to pay him 1 unit of her own payoff in exchange. So Mehmet has to options: • If he accepts Zeynep's offer: they will play the sequential move version of the above game in which Zeynep moves first. Mehmet will receive 1 unit of utility more, and Zeynep will receive 1 unit of utility less (in any outcome of the game) compared to the payoffs given in the bimatrix. 2 • If he rejects Zeynep's offer: they will play the simultaneous move game. a. Represent this strategic interaction in a game tree. b. How many information sets does each player have? c. Characterize the set of pure strategies for both players. d. Present this game as a normal-form game, and characterize the set of pure strategy Nash equi- libria.learn.canterbury.ac.nz Clasarsom Nov 15-ICO EUC LEARN | AKO See the game below and answer the questions 8 to 11: Player-1 C Player-2 X, Y Y Player-1 9 14 8. Player-2 16 17 16 Nash Equilibrium in this game: Select one: O a. Playert: C; Player2: X O b. Playert: C; Player2: Y Oc. Playert: L; Player2: X Od. Playert: L; Player2: Y e. None
- Consider the following simultaneous move game where player 1 has two types. Player 2 does not know if he is playing with type a player 1 or type b player 1. Player 2 C D Player 1 A 12,9 3,6 B 6,0 6,9 C D A 0,9 3,6 B 6,0 6,9 Type a Player 1 Prob = 2/3 Type b Player 1 Prob = 1/3 Find the all the possible Bayesian Nash Equilibriums (BNE) of this game.The bimatrix represents a simultaneous move game between Rowena and Colin. Rowena's payoff is the left number in each cell. ROWENA O O 2 Calculate Rowena 's expected payoff in the mixed strategy Nash equilibrium. 3.5 2.5 Up Down 3 Left 1,16 2,20 COLIN Right 4,6 3,40Tucker and Eddie are playing the following game. Tucker can choose A or B and Eddie can choose C or D. The first payoff is for Tucker, the second for Eddie. Eddie Tucker C D A 3, 2 4, 3 B 4, 5 3, 4 Identify the Nash equilibrium(s) in this game. What rational game theoretic advice would you offer Tucker and Eddie on how to play this game? If Tucker and Eddie follow your advice, what payoff should each expect? Show your work.