2. Two players play the following normal form game. 1\2 Left Middle Right Left Middle Right 4,2 3,3 2,1 3,3 5,5 6,2 1,2 2,6 3,3 Suppose that the game is repeated for two periods. What is the outcome from the subgame perfect Nash equilibrium of the whole game: ○ a) (Left, Left) is played in both periods. ◇ b) (Right, Right) is played in both periods. ◇ c) (Middle, Middle) is played in the first period, followed by (Left, Left) ◇ d) (Middle, Middle) is played in the first period, followed by (Right, Right)
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- 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 ofConsider the following simultaneous move game: Player 1 U M D Player 2 L 2,10 2,5 8,7 C 5,2 11,8 8,4 R 5,4 2,9 8,3 In the Nash equilibrium of this game, player 1 receives a payoff of ✓ and player 2 receives a payoff ofSolve for the Nash equilibrium (or equilibria) in each of the following games. (a) The following two-by-two game is a little harder to solve since firm 2’spreferred strategy depends of what firm 1 does. But firm 1 has a dominantstrategy so this game has one Nash equilibrium. Firm 2 Launch Don’tFirm 1 Launch 60, -10 100, 0 Don’t 80, 30 120, 0 What is the Nash equilibrium of this simultaneous-move game? (b) What would the outcome of this game be if instead firm 1 moved first and then, after seeing what firm 1 chose, firm 2 chose it strategy? In this case firm 1 doesn’t necessarily need to choose a best response, but firm 2 must choose a best response since it moves second.
- 5 Suppose two players play one of the two normal-form games shown in Figure 1. L U 0,-1 D 2,4 R 2,0 6,0 L U | 4,-1 D 2,-2 R 2,0Now suppose that Player 2 knows which game is being played, but Player 1 does not. Find the pure strategy Bayesian Nash equilibrium of this game.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.2. Consider the following game: u 1 r 6,0 0,6 d 3,2 6,0 Are there any Nash equilibria in pure strategies for this game? Find the mixed strategy Nash equilibrium.
- Team 2 plays A Team 2 plays B Team 1 plays A 2, 1 0,0 Team 1 plays B 0,0 1, 2 Consider the game above. Which of the following is a Nash Equilibrium of the game? O Team 1 plays A two thirds of the time and plays the rest of the time, while team 2 plays A two thirds of the time and plays B the rest of the time. Team 1 plays A one quarter of the time and plays B the rest of the time, while team 2 plays A one quarter of the time and plays B the rest of the time. Team 1 plays A one quarter of the time and plays B the rest of the time, while team 2 plays A three quarters of the time and plays B the rest of the time. O None of the other answers are correct. Team 1 plays A two thirds of the time and plays B the rest of the time, while team 2 plays A one third of the time and plays B the rest of the time.Consider the following game : Stag Rabbit Stag 9, 9 0, 8 Rabbit 8, 0 7, 7 The first payoff is that of player 1 and the second that of player 2. a. ) Draw the extensive form of the simultaneous game. Find all the Nash equilibrium. p. Suppose player 1 moves first or we are in a sequential game now. Draw the extensive form in the sequential version. c. What is the subgame perfect Nash Equilibrium (SPNE) in the sequential version? d. ) Explain why it is an SPNE.conside the following game There are two companies that sell Haitian coffee.Each company currently makes $5 million in revenue They need to determine whether they should engage in a social media advertising campaign Advertising costs $2 million for each company If one company advertises and the other does not, then the one that advertises captures $3 million from the company that does not. If both companies advertise they gain nothing. Draw the payoff matrix. What is this games Nash equilibrium
- Team 2 plays A Team 2 plays B Team 2 plays C Team 1 plays A 9, 9 8, 12 6, 6 Team 1 plays B 6, 6 0, 7 5, 5 Team 1 plays C 12, 8 10, 10 7,0 Consider the simultaneous move game above in which two teams are competing against each other. Which of the following statements are true? In all Nash Equilibria of the game Team 2 plays B This game has two Nash Equilibria Team 1's best response to team 2 playing B is to play A. O None of the other answers are correct This game has a mixed strategy Nash Equilibria where a player randomizes over multiple options.(The Beckhams' dilemma) Victoria and David are husband and wife. They both prefer ciean to dirty house but neither likes to clean the house. Their payoffs are given in the table below. Victoria Clean Don't clean 0,8 Clean 5,5 David Don't clean 8,0 1,1 a) Let say they play the clean house game only once, what is the Nash equilibrium? b) Let say Victoria and David has to decide whether to clean or not every day for indefinite number of days. How grim-trigger strategy will be our subgame perfect Nash equilibrium? In other words, what is the patience rate that ensure Victoria and David maintain the cleanliness of the house?1. Two electricity firms compete in the same market and are deciding their level of advertising in order to increase customers and profits. The following matrix shows the profits (in millions) according to the strategy chosen: Firm 1 Strategies Low Advertising Aggressive Advertising Firm 2 Low Advertising 15, 15 20, -2 Aggressive Advertising -2, 20 5,5 a. Identify the one-shot Nash equilibrium. Comment. b. Suppose the players know this game will be repeated exactly 10 times. Can they achieve payoffs that are better than the one-shot Nash equilibrium? Explain. c. Suppose this game is infinitely repeated and the interest rate is 5%. Can the players achieve the collusive outcome? Explain.