T S A 3,1 5,6 B 2,5 3,4 C 4,2 6,3 Consider the following repeated game. The simultaneous move game represented in normal form above is played three times; after each round players observe which strategy profile has been played. Select which is a correct claim among the following ones
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- 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?Consider the following extensive form game between player 1 and player 2. T B (2, 2) L R R (3, 1) (0, 0) (5, 0) (0, 1) (a). Find the normal form representation of this game. (show the bimatrix) (b). Find all pure strategy NE. (c). Which of these equilibria are subgame perfect?GAME UUU B1 Player B B2 A1 7,13 5, 10 A2 3,8 9,16 Player A A3 5,8 4,7 In Game UUU (see table above), assuming players move simultaneously, Player A choosing A1 and Player B choosing B3 is a Nash equilibrium. Player A choosing A3 and Player B choosing B2 is a Nash equilibrium. Both Player A choosing A1 and Player B choosing B1 and Player A choosing A2 and player B choosing B2 are Nash equilibria in pure strategies Player A choosing A1 and Player B choosing B2 is a Nash equilibrium.
- Consider the following simultaneous game: Player 1 U D Player 2 L 20,-10 -10, 20 R -10, 20 20,-10 Please indicate whether each of the following statements is true or false. Player 1 has a dominant strategy. This game has a Nash equilibrium. This game has a Nash equilibrium in pure strategies. Player 1's best response is D if player 2 plays R.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.A game involves two players: player A and player B. Player A has three strategies a1, a2 and a3 while player B has three strategies b1, b2 and b3. Player B b1 b2 b3 a1 -40,30 70,20 -10,120 Player A a2 40,60 80,80 60,20 a3 -30,40 -50,110 150, -70 Assuming that this is a one-time game, answer the following questions: Is there any dominant strategy for each player? What is the secure strategy of each player. What is the Nash equilibrium of the game?
- 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?The following table contains the possible actions and payoffs of players 1 and 2. Player 1 U M D L 2,10 2,5 8,7 Player 2 C 5,2 11,8 8,4 R 5,4 2,9 8,3 This is a simultaneous move game. In a pure strategy Nash equilibrium of this game, Player 1 receives a payoff of ✓and player 2 receives a payoff of If, instead of playing simultaneously, player 2 moves first, then in the Nash equilibrium player 1 receives a payoff of ✓and player 2 receives a payoff ofHelp me please
- Consider the following game: Player 2 In Out Player 1 In -2,-2 2, 0 Out 0, 2 0, 0 (a) What is the Nash equilibrium of this game, or what are the Nash equilibriaof this game? (b) Does either firm have a dominate strategy (a strategy that is always abest response)? Which? (c) Suppose Player 1 could move before Player 2 and Player 2 could observe Player 1’s move. What do you think would happen?Consider a repeated game with the following stage game: Player 1 O O O Cooperate Not Cooperate This game is repeated T-120 times, and t each period both players must choose their actions simultaneously. The players are deciding whether or not to cooperate specifically, whether or not to follow this cooperation strategy: r≤ 3 S|S|AW|N N|H "Each player will play cooperate as long as no one has played Not Cooperate before. If someone has played Not Cooperate before, then each player will play Not Cooperate forever." rs 5 rs Player 2 In this case, cooperation will be possible if the interest rate r is Not Cooperate 5,15 10, 10 None of the above Cooperate 12, 12 15,5Consider the following simultaneous game: Player 1 U D Player 2 L 30,20 -10, -10 R -10, -10 20,30 Please indicate whether each of the following statements is true or false. Player 1 has a dominant strategy. This game has two Nash equilibria in pure strategies. Player 1's payoff in each of the Nash equilibria is 30.