Which of the following games have many Nash equilibria in pure strategies?(A) centipede games; (B) coordination games; (C) prisoner’s dilemma; (D) none of the above.
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Which of the following games have many Nash equilibria in pure strategies?(A) centipede games;
(B) coordination games;
(C) prisoner’s dilemma;
(D) none of the above.
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- Use the following payoff matrix to answer the following questions Suppose this is a one-shot game: a. Determine the dominant strategy for each player. If such strategies do not exist, explain why not. b. Determine the secure strategy for each player. If such strategies do not exist, explain why not. c. Determine the Nash equilibrium of this game. If such an equilibrium does not exist, explain why not.Consider the following normal-form game (a) Calculate the rationalizable set ? (b) Find all Nash equilibria. (c) Find all mixed-strategy Nash equilibria.Problem 1. You are given the following bimatrix games. For each one, find all pure Nash equilibria. (a) (Prisoner's Dilemma) Player 2 Quiet 2, 2 3,0 Fink Quiet Fink 0,3 1,1 Player 1 (b) (Matching Pennies) Player 2 Нead Head 1,-1 Tails -1,1 Player 1 Tails -1,1 | 1, -1 (c) (Battle of the Sexes) Girl OK, football... OK, theatre... Football! Theatre! 1,5 0,0 0,0 5,1 Boy (d) (Battle of the Sexes... modified) Girl Football great, I will invite my dad Theatre! OK, football... OK, theatre... Football! 1,5 0,0 0,0 5, 1 0,0 -1 , 2 Boy
- We have two cable TV companies, Astounding Cable and Broadcast Cable, each simultaneously deciding on a high, medium, or low advertising budget. Their payoffs (in millions) are as follows in the image. True or false? (i) Astounding should play High if Broadcast plays Medium. (ii) This game has a dominant strategies equilibrium. (iii) Astounding playing Medium and Broadcast playing High is a Nash equilibrium.Consider a coordination game where each of two agents picks a number between 1 and 1000. The players get a prize of $1000 each if their numbers are the same, and $0 otherwise. In this game, there exists(A) a thousand of pure-strategy Nash equilibria;(B) an iterated dominant-strategy equilibrium;(C) a dominant strategy equilibrium;(D) none of the above.Which of the following is the COLLUSIVE OUTPUT in the Game Theory Matrix below? * Firm B Payoff = Expected Profit ($m) High Price Low Price High Price $4m; $4m $-1m, $6m Firm A Low Price $6m; $-1m $1m, $1m Both firms choose High Price Both firms choose Low Price Firm A chooses Low Price; Firm B chooses High Price O Firm A chooses High Price; Firm B chooses Low Price
- 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) NoneWhat are the sub games in the following game? Find all subgame perfect Nash equilibria (SPNE)In the game depicted below, firms 1 and 2 must independently (no collusion) decide whether to charge high or low prices. (a) What is the Nash equilibrium for the above game? (b) If the firms were able to collude, what outcome would they settle on? (c) Is there any incentive for Firms 1 and 2 to cheat on the collusive outcome? Please explain.
- Game theory can capture strategic situations where your outcome depends not only upon your own choice but also upon the choice of another. Present a coordination game of your choice where you and another player each have two choices or strategies. Explain in words the Nash Equilibrium concept, and identify the Nash equilibrium or Nash equilibria for your game. Explain why the outcomes that are not Nash equilibria are not.a.) Suppose you manage a large company’s marketing department and are responsible for deciding whether or not to advertise in the Super Bowl. Your team of analysts estimate that for each advertisement, your firm would generate $6 million in additional revenue for the company. It cost $7 million to run a 30-second advertisement. Therefore, your company would expect to lose $1 million in profit for each advertisement. b.) Depict this situation with a game theory payoff matrix. Your company (A) and a major competitor (B) have two potential strategies: to advertise or to not advertise during the Super Bowl. The payoffs in each cell represent the change in firm profits from advertising. Create payoffs in each cell such that the Nash equilibrium is that both firms advertise despite having a higher profit if neither firm advertisedIs the solution to the prisoner’s dilemma game a Nash equilibrium? Why? The solution to the prisoner’s dilemma game is a Nash equilibrium because no player can improve his or her payoff by changing strategy unilaterally. The solution to the prisoner’s dilemma game is not a Nash equilibrium because players do not end up in the best combination for both. The solution to the prisoner’s dilemma game is not a Nash equilibrium because both players can improve their payoffs by cooperating. The solution to the prisoner’s dilemma game is a Nash equilibrium because it is a noncooperative game in which both players have to expect that the other is purely selfish.