See the game below and answer the questions 8 to 11: Player-1 C Player-2 X Player-1 +9 14 Player-2 16 17 16 Nash Equilibrium in this game: Select one: O a. Playert: C; Player2: X b. Playert: C; Player2: Y Oc. Player1: L; Player2: X O d. Player1: L; Player2: Y e. None
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- 12. 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?In game theory, a dominant strategy is the best strategy to pick, no matter which moves are chosen by the other player. O to make the exact same move that was made by the other player. the choice that causes the payoff for the other player to be minimized, regardless of the payoff it earns the best strategy to pick, assuming the other player makes his or her best possible choice. to allocate all personnel resources towards defensive talent in order to dominate opposing offenses. 46°F1. 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 3,3
- 6. Consider the following two-player game: 2 L M U 3,3 2,3 1 M 2,1 3,1 D R 0,2 3,3 0,3 3,0-5, -5 a. Find all pure NE. b. Find a (non-pure) MNE in which player 1 (the row player) plays a pure strategy. c. (Harder Question) Show that there cannot be a CE prescribing that strat- egy D of player 1 (the column player) is played with positive probability.Two politicians from the same party decide whether to support or oppose the gov- ernment's environmental policy. Politician A prefers that they both support, but Politician B prefers that they both oppose. Both politicians agree that the party should have a coherent position and the worst outcome is that one supports and the other opposes the policy. (a) Formulate this situation as a strategic game - specify the players, actions, and payoffs (you can set-up a table of the actions and payoffs). (b) What are the Nash equilibria of this game? Explain your answer.Exercise 6.1Suppose that two airlines decide to collude. Analyse the game between these two companies. Suppose that each of them can charge for tickets a high price or a low price. If one of them charges 100 euros, it gets few profits if the other also charges 100 euros and high profits if the other charges 200 euros. On the other hand, if the company charges 200 euros, it obtains very little profit if the other charges 100 euros and an average profit if the other also charges 200 euros. a) Represent the matrix of results of this game. b) What is the Nash equilibrium in this game? Explain your answer. c) Is there an outcome that would be better than the Nash equilibrium for the two airlines? How could it be achieved? Who would lose out if it were reached?
- し(5,3) b I(2,2) も(0,0) (4,12) a (12.4) (0,0) i). List all subgame pertect Nash equilibria and name one Nash eqvilibrivm that is not subgame pertect i). How many strategies does playot and player 2 have?A game is played as follows: First Player 1 decides (Y or N) whether or not to play.If she chooses N, the game ends. If she chooses Y, then Player 2 decides (Y or N) whetheror not to play. If he chooses N the game ends. If he chooses Y, then they go ahead and playanother game with the payoffs shown below. A player who opts out by choosing N gets 2 andthe other player gets 0. Draw the tree of this game and then find the two subgame-perfect Nashequilibria.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.
- While grading a final exam, an economics professordiscovers that two students have virtually identical answers.She is convinced the two cheated but cannot prove it. The professorspeaks with each student separately and offers the followingdeal: Sign a statement admitting to cheating. If both studentssign the statement, each will receive an “F” for the course. Ifonly one signs, he is allowed to withdraw from the course whilethe other student is expelled. If neither signs, both receive a “C”because the professor does not have sufficient evidence to provecheating.a. Draw the payoff matrix.b. Which outcome do you expect? Why?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.This is the answer.. plz write in hand written Here, the given decision tree shows that player 1 moves either to enter or not to enter, while player 2 has two options to choose that are concede and price war. When analyzing the given information, it can be seen that player 1 will surely enter the market as it will give him higher payoff than the payoff when he does not enter as does not enter gives him $1 billion, while entry will give him either $2 billion or $1.5 billion. Therefore, player 1 will enter. After the entry of player 1, player 2 has an incentive to choose to concede as it will give him the payoff of$1.5 billion, while price war will give him $1 billion. Therefore, the outcome of this game would be: (Enter, Concede)