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- 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. None3 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 85/ Solve the following payoff matrix to find the best strategies and the value of game: BI B2 Al 8 A2 3 5 A3 10 2.
- There are 2 players. They take Ston eS From the Pilt of 6 Stones. Player 1 can takt only 2 or 3 Stones. piayer 2 can taKeS only 2 or 4 StonesS. P layers take turns, observe dil Previous moves, and player 1 mover first. A pla yer loses if She can not make a legal move, While another player ir declared the Winner. Let the pay oF OF Winning egval to 1 and the payoFF OF losing equal to 0. a) represent the in ɛxtemsive Form (depict Only legalmoes) b) Find all SPNE OF this game& explain your a mwwer. Who Will Win ? game Only legalmar)you and a friend decide to run a three mile race. If you agree to run together, you keep up with himfor the first mile, but you overexert yourself and run the last two miles at slower paces on your own. Tomake up for lost time, your friend runs the last two miles at a faster pace. Your mile times are 6:30, 7:00,and 7:30. Your friend’s times are 6:30, 6:00, and 6:00. If you both agree to run on your own, you run aconstant pace of 7:05 while your friend runs at a constant pace of 6:05. If you want to run together butyour friend wants to run solo, he runs his constant pace of 6:05. You, on the other hand, want to showhim that you can run faster, but you end up overexerting yourself after the first mile. You run times of6:20, 7:05, and 7:30. If he wants to run together but you do not, you both run at your pace of 7:05. Thissituation can be turned into an economic game, with the payoffs the overall race times. You each wantto run the fastest time you possibly can.(a) Who are the players in…1\2 U D L 4,3 0,0 R 0,0 2,1 C 1,4 0,0 Q. Suppose players 1 and 2 play the stage game depicted above. Check whether each of these strategies constitute a SPE? 1. Play U,C in Rounds 1 and 2 2. Play D,R in rounds 1 and 2 each 3. Play U,L in Round 1 followed by U,C in Round 2. If Player 2 defects punish by playing D,R in round 2. 4. Alternate between U,C and D,R in Rounds 1 and 2
- QUESTION 9 y a 3, 5 4, 2 4, 1 2, 3 b 2, 4 6, 6 5, 1 1, 2 1,3 7,3 4, 2 3, 7 d 1, 2 5, 2 3, 4 4, 1 How many rationalizable outcomes are there in this game? Give your answer as a whole number. C.19 A decision tee is used when modeling More Chee games in which Sming matters any type of game a prisoners diemma simultaneous decisions < Prey 19 of 30 < KonuşanA st SW B st 2,1 5, 15 2. Consider the game of chicken above. SW 11,4 3,5 a. Find all Nash equilibrium in pure strategies. b. Say that player A uses a mixed strategy, where she picks st with prob. 0.55 and sw with prob. 0.45. What is B's expected payoffs from choosing pure st and pure sw? c. Player B uses a mixed strategy and wants A to choose sw. What is the minimum prob. p, for which B needs to play st so A will choose sw.
- rock paper scissors гock 0. -3 1 рарer 1. -1 scissors -1 3 0. (a) Show that xT= ( ) and yT= (3) together are not a Nash equilibrium 3 3 313 for this modified game. (b) Formulate a linear program that can be used to calculate a mixed strategy x € A(R) that maximises Rosemary's security level for this modified game. (c) Solve your linear program using the 2-phase simplex algorithm. You should use the format given in lectures. Give a mixed strategy x E A(R) that has an optimal security level for Rosemary and a mixed strategy y E A(C) that has an optimal security level for Colin.Consider this extensive form game. The top number is player 1’s payoff, themiddle number is player 2’s payoff, and the bottom number is player 3’spayoff.a. Describe the general form of a strategy for each player.b. Find the SPNE.Game Theory I am trying to assign numbers (theoretical)to a game im making. Its about Tipping. Its based on 3 different efforts a server has showed Can you assign numbers to each of these. This is all made up so you can use whatever values they just need to be in regard to the other values. Thanks. I was thinking to start on high effort Tip could be +10 and no tip could be -10 Best and worst scenario. You do high effort service and get tipped and high effort with no tip. Thanks
