Player 1 Player 2 Player 2 R. Player 1 Player 1 Player 1 Player 1 1,2 3,0 1,2 2,1 0,3 2,2 0,3 2,1 The above game is played. What is the subgame perfect equilibrium? O Player 1 plays L, Player 2 plays L. Player 1 plays a. O Player 1 plays L, Player 2 plays R, Player 1 plays b. O Player 1 plays R, Player 2 plays L, Player 1 plays a. O None of the above
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- In the game below, there are two equilibriums: both players play conserve or both players play plunder. If the game is repeated multiple times, players can maintain equilibrium in which conserve is played if: Player 2 Player 1 Conserve Plunder Select one: a. Conserve 100, 100 50,-100 Plunder -100, 50 0,0 Game is repeated many times and discount rates are high O b. Game is repeated few times and discount rates are low O c. Game is repeated few times and discount rates are high O d. Game is repeated many times and discount rates are low12. Consider a game where each player picks a number from 0 to 60. The guess that is closest to half ofthe average of the chosen numbers wins a prize. If several peopleare equally close, then they share theprize. The game theory implies that (A) all players have dominant strategies to choose 0 (B) all players have dominant strategies to choose 30 (C) there is a Nash equilibrium where all players pick 0 (D) there is a Nash equilibrium where all players pick positive numbers 13. Behavioral data in such games suggests that (A) most subjects choose 0; (B) most subjects choose 30; (C) common answers include 30, 15, 7.5, and 0; (D) most subjects use randomization. Can you help me answer number 13 please?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 scenario to understand the relationship between marginal and average values. Suppose Crystal is a professional basketball player, and her game log for free throws can be summarized in the following table. Fill in the columns with Crystal's free-throw percentage for each game and her overall free-throw average after each game. Game Result Total Game Free-Throw Percentage Average Free-Throw Percentage Game 1 8/10 2 14/20 15/25 18/30 26/40 3 78°F Sunny 4 5 100 On the following graph, use the orange points (square symbol) to plot Crystal's free-throw percentage for each game individually, and use the green points (triangle symbol) to plot her overall average free-throw percentage after each game. Note: Plot your points in the order in which you would like them connected. Line segments will connect the points automatically. (?) O 8/10 6/10 1/5 3/5 8/10 90 F2 -0- @ F3 -0+ # 80 F4 $ F5 H OL % F6 ba 80 A I C F8 & 357 * F10 FO F11 Ea F12 2 Fn Lock Prt Sc +-- F 10:23 A…1. For the following game Player B Player A Left 7,17 10,5 4,4 Middle Right 14,11 4,3 10,25 21,21 Тop Middle 14,4 Bottom 7,3 a) Determine the Nash equilibrium is any? b) Represent the game sequentially starting with player 1 and determine the sub-game perfect equilibrium c) Represent the game sequentially starting with player 2 and determine the sub-game perfect equilibrium d) Find the mixed strategy Nash equilibrium of the following game e) Firm 1 Firm 2 High price Low price High price 4,3 2,4 Low price 2,4 3,3What is the SPNE of the following game, where Player 1 moves first and can play A or B, and player 2 moves second and can play X or Y? Player 1 A B Player 2 Y 3,1 2, 3 1, 2 1, 2 >
- What is Ann's maximin strategy? Game Bob L RAnn U 10,-1 4, 4 D 4, 1 8, -1 Select one: a.none of the other answers b.4/7 U + 3/7 D c.2/5 U+ 3/5 D d.2/7 U + 5/7 D e.3/5 U + 2/5 D4. Consider a two player game with Fred and Barney, who tal turns removing matchsticks from a pile. They start with 33 matchsticks, and Fred goes first. On each turn, ecach player may remove either one, two, three, four, or five matchsticks. The player to remove the last matchstick wins the game. What are the optimal strategies for each player? Who will win? b. Suppose now that they can remove up to six matchsticks, how will the optimal strategies change for- each player? a.Consider the following game: Steffi N K 14, 6 7,6 8, 7 Jim 5, 8 8, 8 13, 6 M 1,5 8, -6 6, 6 What is Jim's best response to Steffi playing P? (you can select more than one answer) V a. K O b. M O c. N O d. L V e. 14 O f. 8
- 1. 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.The next 3 questions involve the following game. There are two players, a husband and wife. They can either be selfish (S) or selfless (U) in their marriage. If they choose to be selfish, then there is a negative ʻguilt’ payoff of g. The payoff matrix is below. Figure 1: The Marriage Game Wife S U S 10-g, 10-g 15-g, 2 U 2, 15-g 12, 12 Number left (right) of comma refers to H's (W's) payoff. 23. Suppose that g = 0. What is the Nash equilibrium (or equilibria)? (A) (S, S). (B) (U, S) and (S, U). (C) (S, S) and (U, U) (D) (U, U). 24. Suppose that g= 5. What is the Nash equilibrium (or equilibria)? (A) (S, S). (B) (U, S) and (S, U). (C) (S, S) and (U, U) (D) (U, U). 25. Suppose that g = 10. What is the Nash equilibrium (or equilibria)? (A) (S, S). (B) (U, S) and (S, U). (C) (S, S) and (U, U) (D) (U, U). Husband3. Suppose that the various Balls of basketball or internet fame Lavar, Lamelo, Liangelo, Lonzo,and Spalding are considering playing in a 1-on-1 tournament. They get a payoff of 0 if theydecide not to participate. The following table illustrates their payoffs across the variousscenarios. 1 Player 2 Players 3 Players 4 Players 5 Players Lavar 10 4 2 -2 -5 Lamelo 10 7 5 2 -1 Liangelo 10 7 5 2 -1 Lonzo 10 8 7 6 5 Spalding 10 9 8 7 6 a. Find and describe all pure strategy Nash Equilibria.b. Suppose now Spalding, since it is in fact a literal basketball, gets a payoff of 0 in anycircumstance, being an inanimate object. The table is now as follows: 1 Player 2 Players 3 Players 4Players 5 Players Lavar 10 4 2 -2 -5 Lamelo 10 7 5 2 -1 Liangelo 10 7 5 2 -1 Lonzo 10 8 7 6 5 Spalding 0 0 0 0 0 Find and describe all pure strategy Nash Equilibria.