Problem 2 Consider the following method of dissolving a partnership. Two partners each own one share of a firm. They have a dispute and each partner wishes to either buy-out, or be bought- out by the other partner. Partner i values both his own and his partner's share at 0; per share. Assume that the 0's are independently and uniformly distributed on [0,1]. Each partner knows his own but not his partner's. The mechanism that the partners agree upon is the following: Each partner bids for the other's share. The highest bidder wins and obtains her part- ner's share for the amount of her winning bid. In the event of a tie, each partner wins with equal probability. (a) Solve for a symmetric equilibrium bidding function in linear strategies, that is, of the form: Is such an equilibrium unique? b(0)=a+ße (b) Suppose the mechanism was modified as follows: The highest bidder wins the oppo- nent's share but pays the amount of the losing bid. Solve for a symmetric linear equi- librium b(.). Discuss whether b() exceeds, equals, or is less than b(); of course, this relationship may vary with 0.

Problem 2 Consider the following method of dissolving a partnership. Two partners each own one share of a firm. They have a dispute and each partner wishes to either buy-out, or be bought- out by the other partner. Partner i values both his own and his partner's share at 0; per share. Assume that the 0's are independently and uniformly distributed on [0,1]. Each partner knows his own but not his partner's. The mechanism that the partners agree upon is the following: Each partner bids for the other's share. The highest bidder wins and obtains her part- ner's share for the amount of her winning bid. In the event of a tie, each partner wins with equal probability. (a) Solve for a symmetric equilibrium bidding function in linear strategies, that is, of the form: Is such an equilibrium unique? b(0)=a+ße (b) Suppose the mechanism was modified as follows: The highest bidder wins the oppo- nent's share but pays the amount of the losing bid. Solve for a symmetric linear equi- librium b(.). Discuss whether b() exceeds, equals, or is less than b(); of course, this relationship may vary with 0.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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