Some Further Problems in Microeconomics

Some Further Problems in Microeconomics - (a What is the...

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Some Further Problems in Microeconomics: (1) Find the Sequential Equilibria of the following game. (2) Draw a game tree that does not exhibit perfect recall. (3) In a standard game of 0’s and X’s how many pure strategies does the first mover have? (Assume that players continue to move until all the entries in the grid are full – although the rules do not require this.) (4) Let 0 < θ <1 be the quality of used cars. Assume this is uniformly distributed. Sellers know the quality of their car buyers only know the average quality of cars supplied. Let p be the price of used cars. A seller of a car quality θ has utility p- θ /2 from selling it at price p and a utility of zero if he does not sell the car. Assume that buyers have utility θ -p if they buy a car of quality θ at the price p. There are not enough cars to supply all potential buyers.
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Unformatted text preview: (a) What is the average quality of cars supplied when the price is p? (b) Show that any price on the interval (0,1/2] is a potential equilibrium price. (c) Suppose now that sellers have utility p-θ 1/2 from selling a car quality θ . What is the equilibrium now? (5) Consider an auction where a seller has 2 units of a good to sell. She will supply one unit to the highest bidder and one unit to the second highest bidder. No buyer wishes to obtain more than one unit. The seller chooses to operate a second price auction – forcing both winning bidders to pay the second highest bid. Is it weakly dominant for the sellers to bid their values? What auction format should the seller use to get the buyers to bid their values? (3,1) (0,0) (1,0) (0,0) (1,1) (1,0) (3,0) (0,1) Action A Action B 1 1 0.9 0.1...
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