Define a dominant strategy and Nash equilibrium. Can two firms interacting with each other have no Nash equilibria if both have a dominant strategy?
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Define a dominant strategy and Nash equilibrium. Can two firms interacting with each other have no Nash equilibria if both have a dominant strategy?
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- Imagine a small town with three car repair shops competing for a limited number of customers. Explain why the three shops working together to keep their prices high is unlikely to be a Nash equilibrium.What is the difference, if any, between a dominant strategy and a Nash equilibrium? Give examples.Two firms operating in the same market must decide between charging a high price or a low price. The Payoffs are as below. Firm A's profit is listed before the comma, B's profit after the comma. Firm B Firm A Low Price High Price Low Price 16, 17 7, 28 High Price 28, 7 22, 22 If each firm tries to choose a price that is optimal, regardless of the other firm's price, what is the Nash equilibrium? Does either firm have a dominant strategy?
- Consider the following extensive form game: Find the Nash equilibrium Find subgame perfect Nash Equilibrium Explain why all Nash equilibriums are not subgame perfectThe following is a static game: Convert this game into dynamic form game. Find the Nash equilibrium and subgame perfect Nash equilibrium of this game. If you consider this game as dynamic then what kind of dynamic game is this.Which of the following is true? A Nash equilibrium is always a perfect subgame equilibrium in a multistage game. A subgame perfect equilibrium is always a Nash equilibrium. A Nash equilibrium is always a subgame perfect equilibrium. Subgame perfect equilibrium and Nash equilibrium are the same concept but with different names.
- Consider a market organized along a 1 mile stretch of road (from D=0 to D=1). Consumers along the stretch of road are uniformly distributed. There are two firms, with Firm 1 located at mile marker .5 and Firm 2 located at mile marker 1.0 and they compete on prices. Customers choose which store to shop at according to P + cD, where c=2 and D is the distance to the store. What is the Nash Equilibrium?Find any Nash equilibria in the game below. Firm B Co-operate Don’t co-operate Firm A Co-operate 60 60 0 80 Don’t co-operate 80 0 10 10 a. There is one Nash equilibrium: both firms don't co-operate. b. There are no Nash equilibria. c. There are two Nash equilibria: one firm co-operates and the other firm doesn't co-operate. d. There are two Nash equilibria: (i) both firms co-operate and (ii) both firms don't co-operate.Find any Nash equilibria in the game below. Firm B Co-operate Don’t co-operate Firm A Co-operate 60 60 0 80 Don’t co-operate 80 0 10 10 Answer a. There is one Nash equilibrium: both firms don't co-operate. b. There are no Nash equilibria. c. There are two Nash equilibria: one firm co-operates and the other firm doesn't co-operate. d. There are two Nash equilibria: (i) both firms co-operate and (ii) both firms don't co-operate.
- The attached diagram depicts two firms controlled by Jacob and Elsa, and two potential actions each firm might take. Payoffs from action combinations appear in the normal-form depiction of the game played by Jacob and Elsa. What is the Nash equilibrium of the game (Jacob's strategy listed first)? a b Jacob's Actions d Dont' Advertise Advertise, Advertise Advertise Don't Advertise J=300 J=400 Don't advertise, Don't advertise Elsa's Actions Don't advertise (Jacob), Advertise (Elsa) с Advertise (Jacob), Don't Advertise (Elsa) E=200 Selected answer will be automatically saved. For keyboard navigation, press up/down arrow keys to select an answer. E=50 Advertise J=100 J=200 E=300 E=100Explain the meaning of a Nash Equilibrium. How does it differ from and equilibrium in dominant strategies?Use the following normal-form game to answer the following questions. a. For what values of x is strategy D (strictly) dominant for player 2? b. For what values of x is strategy B (strictly) dominant for player 1? c. For what values of x is (B, D) the only Nash equilibrium of the game?