In a game, a certain player has m information sets indexed by j = 1,2,...,m. There are kj possible actions for information set j. How many strategies does the player have?
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In a game, a certain player has m information sets indexed by j = 1,2,...,m. There are kj possible actions for information set j. How many strategies does the player have?
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- Suppose there are two players playing a game with east or west and south and nerth ways. Find the expected Nash equilibrium by using the concept of probabilities. Player X Left[L) Right|R) Player Y Up(U) (5,6) (0,8) (4,6) Down[D) (0,9). Ayça and Barış are playing a game and following payoff matrix is for the payoffs of Ayça. Answer the questions according to the following payoff matrix. a) What is the probability that the value of the game is 10?10. Game theory
- 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 1.2. Consider a cheap talk game in which Nature moves by choosing a sender's type, where the type space has four elements: −1, 1, 2, and 3, each occur- ring with equal probability of 1½. The sender learns his type and chooses one of three possible messages: bumpy, smooth, and slick. The receiver observes the sender's message and then chooses one of three actions: 0, 5, and 10. The sender's payoff equals his type multiplied by the receiver's action. The receiver's payoff equals the sender's type multiplied by twice the receiver's payoff. a. Find a separating perfect Bayes-Nash equilibrium. b. Find a semiseparating perfect Bayes-Nash equilibrium.U9. Consider a revised version of the game from Exercise S9: PROFESSOR PLUM Revolver Knife Wrench Conservatory 1,3 2,-2 0,6 MRS. PEACOCK Ballroom 3,2 1,4 5,0 (a) Graph the expected payoffs from each of Professor Plum's strategies as a function of Mrs. Peacock's p-mix. (b) Which strategies will Professor Plum use in his equilibrium mixture? Why? (c) What is the mixed-strategy Nash equilibrium of this game?
- Suppose the payoff matrix was modified such that: Confess Lie About Lie About Confess to Peter / MJ About Knowing Liking Peter Liking Peter Knowing Admit Being 2,2 3,1 8,12 3,14 Spidey Lie About 1,1 4,2 9,8 1,7 Spidey Lie About 4,5 8,6 14,18 4,14 Liking MJ Confess to 5,2 7,1 12,14 5,16 Liking MJConsider the payoff matrix listed below: |1, -1 3, 0 2, 1 |R |0, 3 |1, 2 |0, 0 3, 1 5, 3 2, 1 What is the best response to "R" a. U b. C C. B d. U, C6. 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.
- which is the nash equilibrium? small pig does press large pig does press (20, 130), small pig doesn't press large pig does press (140, 10), small pig does press large pig doesn't press (-5, 150), small pig does not press large pig doesn't press (0,0).Explain what is meant by the last-mover’s advantage.Asap
