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Consider a sealed-bid second-price auction with n buyers whose private values are independent and uniformly distributed over [0, 1].
Find an asymmetric equilibrium at which every buyer wins with probability 1/n .
Can you find an equilibrium at which every buyer i wins with probability αi, for any collection of nonnegative numbers α1, α2,...,αn whose sum is 1?
For what values of p is a 5-component system more likely to operate effectively than a 3-component system?
Give an example of an extensive-form game in which player i has perfect recall and there is a mixed strategy σiwith more than one behavior strategy equivalent to it.
How much effort do the students exert in the Nash equilibrium of the game introduced by Amalia and what value v for the cake induces the students to exert the efficient effort level?
For the game BoS in given Figure, find the max minimizer of each player. Show for each equilibrium, the strategy of neither player guarantees her equilibrium payoff.
Compute the outcome of the unique subgame-perfect equilibrium. - Show that when δ1 = δ2 player 1 has an advantage.
Describe this situation as a game with incomplete information.- Prove that the beliefs of the manufacturers are inconsistent.
Suppose n = 11. Does this game have a Nash equilibrium? If so, describe an equilibrium and explain how many Nash equilibria there are.
What is the smallest value of T for which it possible for B and b to be played in the first play of the game, in a subgame perfect equilibrium
Is it possible for him to be indifferent between the sure payment and the lottery? What is the general lesson to learn from this exercise - Is this preference relation rational in the sense defined by the preference theory?
Find the Nash revision strategies for Ann and Bob which form a SGPNE with the δ identified in part (a) - Verify that the strategies found in part (b) do form a SGPNE
Find the optimal pricing scheme for Tony. Discuss whether Tony would gain from being able to commit to not selling monitors in period 2.
Which firm produces more output in an equilibrium? What is the effect of technical change that lowers firm 2's unit cost c2 (while not affecting firm 1's unit cost c1) on the firms' equilibrium outputs, the total output, and the price?
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