Exercise 1.13. Consider the following game: Player 2 D E F a 2 3 2 2 3 1 Player 1 b 2 0 3 1 1 0 C 1 4 2 0 0 4 (a) Apply the IDSDS procedure to it. Is there a strict iterated dominance equilibrium? GAME THEORY - Giacomo Bonanno 42 12 (b) Apply the IDWDS procedure to it. Is there a weak iterated dominance equilibrium?
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- The ultimatum game is a game in economic experiments. The first player (the proposer) receives a sum of money and proposes a fair proposal (F - 5;5) or unfair proposal (U - 8;2). The second player (the responder) chooses to either accept (A) or reject (R) this proposal. If the second player accepts, the money is split according to the proposal. If the second player rejects, neither player receives any money. 1 A 5:5 2 F R 0:0 U A 8:2 2 1. Find the subgame perfect Nash Equilibrium using backward induction. R 0;0Exercise 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?GAME ZZZ B1 Player B A1 30, 30 Player A A2 20, 40 B2 40, 20 35, 35 In the Game ZZZ (see table above), all payoffs are listed with the row player's payoffs first and the column player's payoffs second. In this game, neither player has a dominant strategy. the Nash equilibrium does not maximize the total payoff. there is no Nash equilibrium. the Nash equilibrium maximizes the total payoff.
- Game Theory de Drew Fudenberg, Jean Tirole. Exercise 2.6**(a) Calculate the safety levels of both players.(b) Find the set of all Nash equilibria (pure and mixed).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)
- Jesse and Janie are playing a game. On the table in front of them, there are 50 coins. They take turns removing some of these coins from the table. At each turn, the person moving can remove either 1,2,3,4,5,6, or 7 coins (they cannot remove 0 or 8, etc.). The person to remove the last coin wins. Suppose Janie is the first player to have a turn (a) In the subgame perfect equilibrium, Janie begins by taking _________coins (b) Suppose Janie makes a mistake in play and removes a number of coins that leaves 27 coins on the table when it is jesses turn. To have a chance at winning, Jesse should remove _________ CoinsUnder what condition can we infer that D is a dominant strategy for Player 1? Player 1 xxy.z0. x>0, y0. U D L x, 0 1, z Player 2 R 0, y z, 1E 11 Continue to maximize profit (0, 80) Stay out Fight entry Enter 12 (0, 10) Continue to maximize profit (30, 50) ($millions entrant's profit, $millions incumbent's profit) In the sequential game shown above, "E" represents the potential entrant firm, and "I" represents the incumbent firm. Firm need to decide whether to enter the market or "stay out". If E stays out, the incumbent is at decision node 11 and simply continues business as usual. If firm E enters, firm I is in decision node 12 and needs to decide whether to "fight entry" or "continue". Payoffs are given in parentheses, with the first term for form E and the second term for firm I. What is the backward induction equilibrium of this game? None of the above are correct. E: Enters; I: (Fights at 11, Fights at 12) E: Stays Out; I: (Continues at 11, Fights at 12) E: Enters; I: (Continues at 11, Continues at 12) E: Stays Out; I: (Continues at 11, Continues at 12)
- Paramter y = 0 What is the highest payoff any player can receive in any subgame perfect Nashequilibrium of the repeated game?• (1,0) (1,1) Player 2 G D H (2,0) Action Player 1 Player 1 Action B Player 1 (3,-1) E Player 2 (0,1) (-1,-1) (a) Find all the Subgame Perfect Nash equilibria in this game. (b) Find all the Nash equilibria in this game. (Hint: write the game in strategic form.)Game Theory Consider the entry game with incomplete information studied in class. An incumbent politician's cost of campaigning can be high or low and the entrant does not know this cost (but the incumbent does). In class, we found two pure-strategy Bayesian Nash Equilibria in this game. Assume that the probability that the cost of campaigning is high is a parameter p, 0 < p < 1. Show that when p is large enough, there is only one pure-strategy Bayesian Nash Equilibrium. What is it? What is the intuition? How large does p have to be? Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.