The only strategies that remain after iterated deletion of dominated strategies are those that ... ... are the dominant strategies. ... should be played with equal probability as a mixed strategy. ... could be best responses under some belief about the other players' strategies, assuming everyone is acting rationally. O... yield the same expected payoff against the most likely combination of the other players' strategies.
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- Two firms, X and Y, are planning to market their new products. Each firm can develop TV, Laptop. Market research indicates that the resulting profits to each firm for the alternative strategies are given by the following payoff matrix : MATRIX IS ATTACHED Find the Nash equilibria for this game, assuming that both firms make their decisions at the same time. (explain the decision step by step) If each firm is risk averse and uses a maximin strategy, what will be the resulting equilibrium? (explain the decision step by step) What will be the equilibrium if Firm X makes its selection first? If Firm Y goes first?Game Theory Consider the entry game with incomplete information studied in class. An incumbent politician's cost of campaigning can be high or low and the entrant does not know this cost (but the incumbent does). In class, we found two pure-strategy Bayesian Nash Equilibria in this game. Assume that the probability that the cost of campaigning is high is a parameter p, 0 < p < 1. Show that when p is large enough, there is only one pure-strategy Bayesian Nash Equilibrium. What is it? What is the intuition? How large does p have to be? Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.A total of n ≥ 2 companies are considering entry into a new market. The cost of entry is 30. If only one company enters, then its gross profit is 200. If more than one company enters, then each entrant earns a gross profit of 40. The payoff to a company that enters is its gross profit minus its entry cost, while the payoff to a company that does not enter is 60. Find a symmetric Nash equilibrium in mixed strategies.
- 1 \ 2 a b c A 2,2 2,1 0,0 B 3,1 3,0 1,3 C 1,3 3,2 3,1 a) Eliminate iteratively all strictly dominated strategies. b) Find all Nash equilibria. c) What is the player 1’s best response to the strategy σ2 = (z , ½ , ½ - z) of player 2, where z is a parameter that lies in the closed interval [0, ½]. d) Compute the payoffs to player 1 and to player 2 for their respective strategy profiles σ1 = (0,½,½) and σ2 = (½,0,½).4. You have probably had the experience of trying to avoid encountering someone, whom we will call Rocky. In this instance, Rocky is trying to find you. It is Saturday night and you are choosing which of two possible parties to attend. You like Party 1 better and, if Rocky goes to the other party, you get a payoff 20 at Party 1. If Rocky attends Party 1, however, you are going to be uncomfortable and get a payoff of 5. Similarly, Party 2 gives you a payoff of 15, unless Rocky attends, in which case the payoff is 0. Rocky likes Party 2 better, but he is likes you. He values Party 2 at 10, Party 1 at 5, and your presence at either party that he attends is worth an additional payoff of 10. You and Rocky both know each others strategy space (which party to attend) and payoffs functions.Market Entry: Three firms are considering entering a new market. The payoff for each firm that enters is 0, where n is the number of firms that enter. The cost of entering is 62. Find all the pure-strategy Nash equilibria. b. Find the symmetric mixed-strategy equilibrium in which all three players enter with the same probability.
- Nike and Adidas face the following coordination problem in trying to decide whether to conduct heavy or light combative advertising against the other firm. Adidas Light Ads Heavy Ads Nike Light Ads $20 M, $24 M $10 M, $8 M Heavy Ads $8 M, $12 M $16 M, $18 M Assuming that both companies announce their strategies simultaneously, which of the following set of strategies are Nash equilibrium? Check all that apply. ○ {Light Ads with Probability = 0.5909, Light Ads with Probability = 0.6222} O {Light Ads A, Heavy Ads N} O {Light Ads with Probability = 0.4545, Light Ads with Probability = 0.4444} O {Heavy Ads A, Light AdsN} O {Light Ads, Light Adsµ} ○ {Heavy Adsµ, Heavy Adsµ}Experiments suggest that subjects in centipede games would (A) always stop the game in the fifirst round; (B) always choose the iterated dominant-strategy equilibrium strategy; (C) typically pass the move a few times and then stop the game before the last round; (D) never stop the game.Consider the two-person Stag Hunt game. First, find each player’s best response functions; then plot the best response functions and find all Nash equilibria, including both pure-strategy and mixed-strategy equilibria.
- Consider a Vickery auction. There are N bidders, each of them values the object £vi, with i = 1…N. Each bidder can submit a bid in a sealed envelope. Once all the bids have been made, the envelopes are opened. The winner of the auction is the bidder who made the highest bid, however, s/he pays the second-highest bid. What are the weakly dominant strategies in this game? Is there only one?Find the Nash Equilibria for each of the following 2x2 games (The left payoff value is associated with the strategies (1 or 2) while the right payoff value is associated with the strategies (A or B)): (a) (b) (c) (d) B 1 3,3 2 4,4 5,5 1 2 1 2 1 2 A 2,2 24 A B 2,5 0,3 4,0 -5,2 A 1,0 0,6 B 4,1 5,5 A B -1,-3 -3,2 -4,1 0,0Parameter z = 1 How many pure strategy profiles exist in this game?