Each of Player 1 and Player 2 chooses an integer from the set {1, 2, ..., K}. If they choose the same integer, P1 gets +1 and P2 gets -1; if they choose different integers, P1 gets -1 and P2 gets +1. (a) Show that it is a NE for each player to choose every integer in {1, 2, ..., K} with equal probability, K1 . (b) Show that there are no NE besides the one you found in (a).
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Each of Player 1 and Player 2 chooses an integer from the set {1, 2, ..., K}. If they choose the same integer, P1 gets +1 and P2 gets -1; if they choose different integers, P1 gets -1 and P2 gets +1.
(a) Show that it is a NE for each player to choose every integer in {1, 2, ..., K} with equal probability, K1 .
(b) Show that there are no NE besides the one you found in (a).
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- Pag question Player 2 Y1 Y2 Y3 X1 8,5 6,4 11,4 4,8 5,6 Player 1 X2 7,5 12,4 3,3 X3 4,6 For the game given above, ((p1.p2.p3).(q1.q2.q3) is a mixed strategy: The first triplet is Piayer 1's probability allocations to X1, X2, X3. The second triplet is Player 2's probability allocations to Y1, Y2, Y3. Which of the following is true? O a. For Player 2, Y1 is strictly dominated by Y2 Ob. ((p1.p2.p3),(q1.42.q3))- (2/5.2/5,1/5)(3/5.1/5,1/5) is a mixed NE Oc. No action is strictly dominated by any mixed strategy O d. ((pl.p2.p3).(q1.q2.q3)- (1/4.2/4,1/4C/4,0,1/4) is a mixed NEPlayer 2 Y1 Y2 Y3 X1 1,4 8,4 7,4 6,2 4,5 Player 1 X2 3,5 3,5 X3 5,3 2,2Player 2 Y1 1,4 3,5 5,3 X1 Y2 Y3 Player 1 8,4 7,4 6,2 X2 4,5 3,5 2,2 X3 For the game given above, ((p1.p2,p3).(q1.q2.q3) is a mixed strategy: The first triplet is Player 1's probability allocations to X1, X2. X3. The second triplet is Player 2's probability allocations to Y1, Y2. Y3. Which of the following is true? O a. There are only pure NEs in this game O b. ((p1,p2.p3).(q1.q2.q3))- ((1/3,1/3,1/3)(1/3.0.2/3) is a mixed NE Oc (pt.p2.p3).(q1.q2.q3))- ((1/3.2/3,0)(1/3,1/3,1/3)) is a mixed NE O d. No action is strictly dominated by some mixed strategy 到
- If Firm 1 chooses to release the console in October with probability of 0.692 or December with a probability of 0.308, then Firm 2 is indifferent between choosing a release date. If Firm 2 released the console in October with probability of 0.50 or December with a probability of 0.50, then Firm 1 is indifferent between choosing a release date Suppose now that instead of choosing the release date at the same time, the firms choose sequentially (but still in advance). Firm A chooses its release date first, then firm B observes that date and chooses its own date. Thepayoffs are otherwise the same as above. Represent the game tree corresponding to this dynamic game.a) For a group of 300 cars the numbers, classified by colour and country of manufacture, are shown in the table. Black Silver White Korea 33 34 35 Japan 23 9 24 America 16 25 34 Germany 19 16 32 One car is selected at random from this group. Find the probability that the selected car is (i) Is Silver car from Germany (ii) a black or white car manufactured in Korea. (iii) not manufactured in Japan. (iv) is a white car, given that it was manufactured in America. (v) Are the events 'Korea' and 'Black' Mutually Exclusive? Justify your response.A bunch of cookies should be divided among students by a teacher. Each student writes secretly on a sheet of paper his name and the amount of the cookies (his bid) he wants to get (other students cannot see this number). Then the teacher sorts these bids in ascending order and gives cookies to the students starting from the bid with the smallest amount. If cookies are finished at some point the rest of the students get nothing. If there are several equal bids that cannot be satisfied simultaneously with the current amount of cookies, cookies are equally divided among the students who named these bids. If there are extra cookies, the teacher keeps them. You should assume that cookies are perfectly divisible. Find a Nash Equilibrium in pure strategies. Explain why the set of strategies you propose is indeed a Nash Equilibrium in pure strategies. Explain why there are no other Nash equilibria.
- David Barnes and his fiancée Valerie Shah are visiting Hawaii. At the Hawaiian Cultural Center in Honolulu, they are told that 2 out of a group of 8 people will be randomly picked for a free lesson of a Tahitian dance a. What is the probability that both David and Valerie get picked for the Tahitian dance lesson? (round 4 decimal places) b. What is the probability that Valerie gets picked before David for the Tahitian dance lesson? (round 4 decimal places)(b) Consider the simultaneous-move game below with two players, 1 and 2. Each player has two pure strategies. If a player plays both strategies with strictly positive probability, we call it a strictly mixed strategy for that player. Show that there is no Nash equilibrium in which both 1 and 2 play a strictly mixed strategy. Player 2 b₁ b₂ Player 1 a₁ 3,0 0,1 a2 2,1 2,1For a group of 300 cars the numbers, classified by colour and country of manufacture, are shown in the table. Black Silver White Korea 33 34 35 Japan 23 9 24 America 16 25 34 Germany 19 16 32 One car is selected at random from this group. Find the probability that the selected car is a black or white car manufactured in Korea. not manufactured in Japan. is a white car, given that it was manufactured in America. Are the events ‘Korea’ and ‘Black’ Mutually Exclusive? Justify your response. Are the events ‘Korea’ and ‘Black’ Independent? Justify your response
- Two coins are tossed 500 times, and we get: i) Two heads: 105 times ii) One head: 275 times iii) No head: 120 times Find the probability of each event(ii) A mixed strategy profile (p, q) is one in which p = (p,P2.... P) is the mixed strategy of player 1, and q- (g1, q2,..q4) is the mixed strategy of player 2. Show that if p, >0 in a Nash equilibrium profile (p*, q*), the player 2 must also play i with strictly positive probability q'; > 0. (State clearly any theorem you use to show this. You are not required to justify the theorem.) %3DPlease do not give solution in image format thanku Two Manufacturers supply food to a large cafeteria. Manufacturer A supplies 40% of the soup served in the cafeteria, while Manufacturer B supplies 60% of the soup that is served. 3% of the soup cans provided by Manufacturer A are found to be dented, while 1% of the cans provided by Manufacturer B are found to be dented. Given that a can of soup is dented, find the probability that it came from Manufacturer B.