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) Fancy, Casual = (7, 2) O Casual, Casual = = (9,7) Fancy, Fancy=(3, 6) 7,2 9,7
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- Player 2 E F H A 6, 5 6, 7 9, 6 7,6 В Player 1 C 6, 7 6, 9 8, 5 9, 7 5, 8 5, 6 7,5 7,5 7,9 8, 7 11, 6 5, 6 (1) In the Unique Nash equilibrium of this game, which strategy does Player1 play? And why? (2) In the Unique Nash equilibrium of this game, which strategy does Player2 play? And why? (3) Is this game dominance solvable? And Why? (4) Does this game have at least one inadmissible Nash equilibrium? And Why?Costco Spend $1B on advertising Spend $1.5B on advertising Spend $1B on advertising $3.5B; $2.7B $4.2; $2.2B Target Spend $1.5B on advertising $3.2B; $3.4B $4B; $3B9. Find all of the Nash equilibria for the three-player game here. Player 1 a b Player 3: A Player 2 X y Z 1,1,0 2,0,0 2,0,0 3,2,1 1,2,3 0,1,2 2,0,0 0,2,3 3,1,1 Player 1 a b C Player 1 Player 3: C X Player 2 y 2,0,0 0,1,2 0,1,1 1,2,1 3,1,2 0,1,2 a b C Player 3: B Player 2 X 2,0,0 1,2,0 0,1,2 Z 0,1,2 0,1,2 1,1,2 y 0,0,1 1,2,1 2,2,1 Z 2,1,2 1,2,1 2,1,0
- 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 3,40Exercise 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.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…
- 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. NoneL 0 4 15.1 X₂ A M R 0 1 4 0 2 B L 4 0 с X3 M R 0 1 3 FIGURE 15.5 Exercise 15.1. Equilibrium Selection: Consider the extensive-form game in Figure 15.5. a. Find all the Bayesian Nash equilibria of this game. b. Which of the Bayesian Nash equilibria are also perfect Bayesian equi- libria? Why?1. Find all mixed strategy Nash Equilibria for the games below. How many Nash Equilibria do these games have (including both pure and mixed strategy)? Player 2 A) R Player 1 2,2 4,1 E 1.4 3,3 B) Player 2 X y a 4,0 2,1 3,2 Player 1 b 2,2 3,4 0,1 2,2 1,2 0,3 c) Player 3: A Player 2 X y a 2,0,4 1,1,1 1,2,3, Player 1 3,2,3 0,1,0 2,1,3 b 1,0,2 0,0,3 3,1,1 Player 3: B Player 2 X y 2,0,3 4,1,2 1,2,2 a Player 1 b 1,3,2 2,2,2 0,4,0 0,0,0 3,0,3 2,1,0
- 1. Consider the game where initially She chooses between "Stay Home" and "Go Out". If She chooses "Stay Home" then She gets 2 and He gets 0. If She chooses "Go Out" then they each simultaneously choose "Movie" or "Concert" where the payoffs are 0,1 or 3 as in the Battle of the Sexes Game. What are the subgame perfect Nash Equilibria of this game ?3 0: she makes a pront of $9 An is ISK AVCise and aunty she makes. Let P be the probability that it rains the day of the concert. Find the number P tha makes Ann indifferent between organizing the concert in the Club or at the Park. 8. Compute the mixed strategy Nash equilibrium of the game below: Bungle F2 # Zippy E Left Right DOD F4 Up 2,-1 R I 20 F3 $ BAG 3 4 -2,0 HOT % 5 F5 Down 3,1 T 4,-2 VO MacBook Air 6 F6 Y & 7 F7 * U 81. Consider the following sequential game: Left (3,5) Mary Go (6,4) Up Right John Stop (5.7) John (a) Draw the game tree of the game. John Go Down (4,1) Left Mary Stop (2,5) Right (6,-1) (John as player 1 and Mary as player 2) By backward induction, find a Nash equilibrium and the corresponding payoffs. 2. Eve and Noa start with $10 in each of their piles. They take turns choosing one of two actions, continue or stop, with Eve choosing first. Each time a player says continue, $10 will be removed from her pile, and $20 will be added to the other player's pile. The game automatically stops when the total amount in their piles reaches $60. (Eve as player 1 and Noa as player 2) (b) By backward induction, find a Nash equilibrium and the corresponding payoffs.
