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- Consider the following simultaneous game: Player 1 U D Player 2 L 30,20 -10, -10 R -10, -10 20,30 Suppose player 1 plays a mixed strategy in which she plays U 25% of the time and D 75% of the time, and player 2 plays a mixed strategy in which she plays L 25% of the time and R 75% of the time. This pair of strategies ✓a Nash equilibrium. Player 1's expected payoff from playing U (when player 2 plays the mixed strategy above) isConsider the extensive form game shown below. At each terminal node, the first payoff belongs to player 1, the second payoff belongs to player 2, and the third payoff belongs to player 3. How many strategies does player 3 have in this game? Numerical answer (12 (2,2,1) 2 b₂ (22, (2,4,2) (4,2,3) b₁ 2 (3,3,3) C1 02/ 03 b2 b3 (2,2,1) (4,2,0) (2,0,2) 03 3 b3 (0,3,4) image 1GAME UUU B1 Player B B2 A1 7,13 5, 10 A2 3,8 9,16 Player A A3 5,8 4,7 In Game UUU (see table above), assuming players move simultaneously, Player A choosing A1 and Player B choosing B3 is a Nash equilibrium. Player A choosing A3 and Player B choosing B2 is a Nash equilibrium. Both Player A choosing A1 and Player B choosing B1 and Player A choosing A2 and player B choosing B2 are Nash equilibria in pure strategies Player A choosing A1 and Player B choosing B2 is a Nash equilibrium.
- 9 00 3 -2 -8 A = ( ) and B = 03 -5 -2 Let I be the bimatrix game whose payoffs are described by A for the row-player and B for the column- player. 1. Compute all mixed Nash equilibria of T. 9ITERATIVE DOMINANCE Consider the following game in strategic form. a₁ 22 a3 bi 35,52 30,30 28,9 (9,11) (45,47) (47,28) (52,16) (28,9) (30,30) (16,45) (11,35) (35,52) b2 11,35 9,11 16,45 b3 52,16 45,47 47,28 Which of the following payoff profiles survive iterative deletion of strictly dominated strategies? (Mark all profiles that survive.)In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second (36-40). GAME 5 Player B B1 7,3 A2 3,8 Player A A1 In Game 5 above, in the Nash equilibrium in mixed strategies player A chooses A1 with a 5/9 probability. player A chooses A1 with a 2/9 probability. player A chooses A1 with a 3/9 probability. O player A chooses A1 with a 4/9 probability. B2 5, 10 9,6
- Consider a repeated game in which the stage game in the following figure is played in each of two periods and there is no discounting. R U 8, 8 0,9 0,0 9,0 0,0 3, 1 D 0,0 1, 3 -3,-3 Fully describe a subgame perfect equilibrium in which the players select (U, L) in the first period.MIXED STRATEGY NASH EQUILIBRIUM Consider the following game in strategic form. b1 b2 a1 18,2 80,60 a2 40,60 2,18 1-п 1-0 This game has a mixed strategy Nash equilibrium (T*,o*) in which each player uses both pure strategies with strictly positive probability. Find the value of o*-n*. (Please report your answer in decimal form, rounded if necessary to the nearest 0.01.)10 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 ?
- A game involves two players: player A and player B. Player A has three strategies a1, a2 and a3 while player B has three strategies b1, b2 and b3. Player B b1 b2 b3 a1 -40,30 70,20 -10,120 Player A a2 40,60 80,80 60,20 a3 -30,40 -50,110 150, -70 Assuming that this is a one-time game, answer the following questions: Is there any dominant strategy for each player? What is the secure strategy of each player. What is the Nash equilibrium of the game?Paramter y = 0 If ⟨a, d⟩ is played in the first period and ⟨b, e⟩ is played in the second period, whatis the resulting (repeated game) payoff for the row player?The following game is played by 2 players Jack Left Middle Right Adam Up 1,2 3,5 2,1 Middle 0,4 2,1 3,0 Down -1,1 4,3 0,2 a) Determine all dominant strategies for Adam and Jack. b) Solve the equilibrium for this game. 5/5 节:1/1 字数:1132 拼写检查 タ文档未保护 正在备份 口目 目 同 MacBook
