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Parameter z = 1
How many pure strategy profiles exist in this game?
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- Two firms, Tim Horbucks and Startons, consider enter the market for take-out coffee, or not. The profit each firm can make (in dollars) is indicated in the table below, where the fixed cost of producing is F dollars. What is the largest value of F below which the game has a UNIQUE Nash equilibrium in pure strategies? Startons Enter Not Enter Enter 400 - F, 400 - F 600 - F,0 Tim Horbucks Not Enter 0, 600 - F 0 ,0 Enter a positive number below, in dollars.QUESTION 2 In the game above, what is/are the sub-game perfect Nash equilibrium? (up, up) (up, down) ( down, up) (down, down) No equilibrium exists QUESTION 2 Up Down Player 1 No equilibrium exists Up In the game above, what is/are the sub-game perfect Nash equilibrium? (up,up) (up,down) (down, up) □ (down, down) Down Up Down Player 2 P1 gets $45 P2 gets $155 P1 gets $100 P2 gets $10 P1 gets $85 P2 gets $85 P1 gets $95 P2 gets $95Two firms are competing to establish one of two new wireless communication standards, A or B. A strategy is a choice of standard, and an outcome of this game is a choice of standard by each firm – for example, (A, B) represents the case where Firm 1 decides to develop standard A and Firm 2 develops standard B. Here, the first letter will always correspond to Firm 1’s decision, and the second letter to Firm 2’s decision. Firm 1 has the following preferences over outcomes, in order of highest to lowest preferred: it prefers (A, A) to (B, A) to (A, B) to (B, B). Firm 2 prefers (A, B) to (A, A) to (B, A) to (B, B). Suppose that firms simultaneously decide which standard to develop. What is the pure strategy Nash equilibrium?
- Problems associated towards unique outcomes in games where multiple Nash equilibria exist”Problem 2. Consider the partnership-game we discussed in Lecture 3 (pages 81-87 of the textbook). Now change the setup of the game so that player 1 chooses x = [0, 4], and after observing the choice of x, player 2 chooses y ≤ [0, 4]. The payoffs are the same as before. (a) Find all SPNE (subgame perfect Nash equilibria) in pure strategies. (b) Can you find a Nash equilibrium, with player 1 choosing x = 1, that is not subgame perfect? Explain.Finding Nash Equilibria Consider the following two player, normal form game: Player 1 Player 2 C L (2,1) U M (-2,-2) D R (2, -1) (1,2) (-1, 1) (0,0) (3,1) (0,0) (-1,-1) Find all pure and mixed strategy Nash equilibria. Calculate each player's expected payoffs at each equilibrium.
- For the game below, find all mixed-strategy Nash equilibria.Up Down Up Up Down Down Player 1 Player 2 In the game above, what is/are the EFFICIENT sub-game perfect Nash equilibrium? (up,up) (up,down) (down, up) (down, down) No EFFICIENT equilibrium exists P1 gets $45 P2 gets $155 P1 gets $100 P2 gets $10 P1 gets $85 P2 gets $85 P1 gets $95 P2 gets $95John and Paul are walking in the woods one day when suddenly an angry bear emerges from the underbrush. They each can do one of two things: run away or stand and fight. If one of them runs away and the other fights, then the one who ran will get away unharmed (payoff of 0) while the one who fights will be killed (payoff -200). If they both run, then the bear will chase down one of them and eat them to death but the other one will get away unharmed. Assuming they don't know which one will escape we will call this a payoff of -100 for both. If they BOTH fight, then they will successfully drive off the bear but they may be injured in the process (payoff -20). Construct a payoff matrix for this game and identify the pure strategy Nash equilibrium. (Indicate it with words not with a circle!)
- Consider a simultaneous game where player A has a dominant strategy and player B has two strategies (none of which is a dominant strategy). How many pure strategy Nash equilibria will this game have? A) Exactly 1 B) Exactly 2 C) Either 1 or 2 D) NoneTeam 2 plays A Team 2 plays B Team 1 plays A 0, 24 10, 10 Team 1 plays B 4, 4 24, 0 Consider the infinitely repeated version of the game above. Which of the following is the smallest discount factor such that the grim trigger strategy under which team 1 plays A and team 2 plays B until a team deviates, after which team 1 plays B forever and team 2 plays A forever is a Nash Equilibrium? 1/100 1/2 3/4In a small town there are two pizza restaurants . If neither restaurant advertises, its revenue will not change. If only one firm advertises, the firm that advertises will double its revenue and the firm that doesn't advertise will see a decrease in its revenue, but if both firms advertise, their revenue will not change. What outcome would be predicted by game theory in this market? Both restaurants will advertise. Game theory would predict chat sometimes one restaurant would advertise, and the rest of the time both will advertise. Neither restaurant will advertise Game theory is only a theory and cannot predict real-world events. One restaurant will advertise.