Economic Theory Microeconomics Sequence
Economic Theory Microeconomics Sequence ECON 713
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This 1 page Class Notes was uploaded by April Jerde on Thursday September 17, 2015. The Class Notes belongs to ECON 713 at University of Wisconsin - Madison taught by Staff in Fall. Since its upload, it has received 60 views. For similar materials see /class/205156/econ-713-university-of-wisconsin-madison in Economcs at University of Wisconsin - Madison.
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Date Created: 09/17/15
Econ 713 Discussion Week 15 05 11 07 Danqing Hu XL Michael Rapp 1 The Myerson Satterthwaite Theorem Theorem 1 MyersonSatterthwaite Consider a bilateral trade setting in which the buyer and the seller are risk neutral the valuations 91 and 92 are independently drawn from the intervals 131 C R and 232 C R with strictly positive densities and 131 N 232 7E Q Then there is no Bayesian incentive compatible social choice function that is ex post e cient and gives every buyer type and every seller type nonnegative expected gains from participation Exercise 1 MWG 23E6 Consider a bilateral trading setting in which both agents initially own one unit of a good Each agent is i12 valuation per unit consumed of the good is 9239 Assume that 9239 is independently drawn from a uniform distribution on 07 1 1 Characterize the trading rule in an ex post e cient social choice function 2 Consider the following mechanism Each agent submits a bid the highest bidder buys the other agent s unit ofgood and pays him the amount of the highest bid Derive a symmetric Bayesian Nash equilibrium of this mechanism Hint39 Look for one in which an agent s bid is a linear function of his type 5 What is the social choice function that is implemented by this mechanism Verify that it is Bayesian incentive compatible Is it ex post e cient Is it individually rational which here requires that Ui gt 9239 for all 9239 and i 12 Exercise 2 MWG 23E7 Consider a bilateral trade setting in which the buyer s and seller s valuations are drawn independently from the uniform distribution on 07 1 N Show that iff is a Bayesian incentive compatible and interim individually rational social choice that is exipost e cient the sum of the buyer s and seller s expected utilities under f cannot be less than 6 N Show that in fact there is no social choice function whether Bayesian incentive compatible and interim individually rational or not in which the sum of the buyer s and seller s expected utilities exceeds 5
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