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Harry (Player I) is to choose between the payoff vector (2, 1) and playing the following game, as a row player, against Harriet (Player II), the column player:
(a) What are Harry's pure strategies in this game? What are Harriet's?
(b) What are the Nash equilibria of the game?
(c) What is the set of correlated equilibria of the game?
What is the average length of time a car is in the yard, in the bump area, and in the painting area? What is the average length of time from when a car arrives until it leaves?
If player 1 is not type ß, then what probability would player 1 assign to the event that a letter sent by player 1 was lost in the mail? Show that there is no Bayesian equilibrium of this game in which player 2 ever chooses x2.
Show that the game has a mixed strategy Nash equilibrium in which each player chooses each positive integer up to K with probability 1/K.
One airport had 28% late arrivals. After a new directing system was installed, a sample of 1200 flights had 322 late arrivals. At the .01 level, did the new system lower the rate of late arrivals? List the null and alternate hypotheses.
Suppose that player 1 selects the strategy p = 50 and player 2 selects the cutoff-rule strategy with p - = 50. Verify that these strategies form a Nash equilibrium of the game. Do this by describing the payoffs players would get from deviating.
Represent this game in the extensive and normal forms. - Find the pure-strategy Nash equilibria of this game. - Calculate the mixed-strategy Nash equilibria and note how they depend on x.
Find the maxmin value and the maxmin strategy (or strategies) of the players. Does this game have an equilibrium? If so, find it.
Solve for the Nash equilibrium of G. What if the game is repeated for two periods. Find the SPNE. Is cooperation (C, C) sustainable for some value of x
Prove the following claims for n-player extensive-form games:- Adding information to one of the players does not increase the maxmin or the minmax value of the other players.
Find all the subgame perfect equilibria of this game, assuming that both Hillary and Bill are risk-neutral, i.e., each of them seeks to maximize the expected payoff he or she receives.
Show that army 2 can increase its subgame perfect equilibrium payoff (and reduce army 1's payoff) by burning the bridge to its mainland, eliminating its option to retreat if attacked.
Consider the two-period repeated game in which this stage game is played twice and the repeated-game payos are simply the sum of the payos in each of the two periods.
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