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Nash equilibria of the centipede game:-
Show that the outcome of every Nash equilibrium of this game is the same as the outcome of the unique subgame perfect equilibrium (i.e. player 1 stops the game immediately). The logic that in the only steady state player 1 stops the game immediately is unassailable. Yet this pattern of behavior is intuitively unappealing, especially if the number k of periods is large.
The optimality of player 1's choosing to stop the game depends on her believing that if she continues, then player 2 will stop the game in period 2. Further, player 2's decision to stop the game in period 2 depends on her believing that if she continues then player 1 will stop the game in period 3. Each decision to stop the game is based on similar considerations.
Consider a player who has to choose an action in period 21 of a 100-period game, after each player has continued in the first 20 periods. Is she likely to consider the first 20 decisions-half of which were hers-"mistakes"?
Or will these decisions induce her to doubt that the other player will stop the game in the next period? These questions have no easy answers; some experimental evidence is discussed in the accompanying box.
Does this game have a pure-strategy Nash equilibrium? -Find the mixed-strategy Nash equilibrium. - Describe the equilibria of the game in which player 1's extra satisfaction from selecting box A is equivalent to receiving $120.
Determine the solution to the given advertising decision game between Coke and Pepsi, assuming the companies act independently.
Construct a diagram that shows the payoffs to the two firms in strategic (normal) form. What is the Nash equilibrium in this game?
Is it a strictly dominant strategy to bid your true valuation in this auction? Is it a weakly dominant strategy to bid your true valuation in this auction?
Is this preference relation rational in the sense defined by the preference theory - Is this preference relation rational in the sense defined by the expected utility theory?
What values of p1 and p2 are needed to make (C, C) a Nash equilibrium of the induced game? - Compare the unilateral commitments described here with contracts.
What is game theory? What is a Nash Equilibrium or Nash equilibriums in this game?
Find all the Bayesian Nash equilibria of this game. - Which of the Bayesian Nash equilibria are also perfect Bayesian equilibria? Why?
What is firm 2's optimal quantity as a function of q1, conditional on entry? - Compute the subgame perfect Nash equilibrium of this game.
In a two player, one shot simultaneous move game each player can select strategy A or B. If both players select strategy A, each receives a payoff of $500.
Find the symmetric Nash equilibrium of this n-player normal-form game. - Compute the probability that at least one person calls for help in equilibrium.
Test the hypothesis that random variable 30.4 31.2 30.8 29.9 30.4 30.7 29.9 30.1 come from a normal distribution with mean 30.5. The standard deviation of the measurements is known to be 0.1
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