Two bidders compete in a sealed-bid auction for a single indivisible object. For each bidder i, the valuation of the object is uniformly distributed on [0, 1]. The valuations of the two bidders are independent. Each bidder knows her own valuation, but not the valuation of the other bidder. The bidders simultaneously submit bids b € [0, ∞), and whoever submits the higher bid wins the object and pays the average of the two bids. In case of a tie, each bidder wins the object with probability 1/2 and again the winner pays the average of the two bids. Find a Nash equilibrium of this game in which each bidder's strategy is linear in her valuation. Solution: Look for a symmetric equilibrium where each player bids according to b(v) = av+c. First note that in equilibrium, b(0) = 0 since otherwise types with valuations just above 0 win with positive probability and pay more than their valuation, and hence would prefer to lower their bids. Hence e=0. For every valuation vi for player 1, v₁ = ' must solve max Pr(b₂

Two bidders compete in a sealed-bid auction for a single indivisible object. For each bidder i, the valuation of the object is uniformly distributed on [0, 1]. The valuations of the two bidders are independent. Each bidder knows her own valuation, but not the valuation of the other bidder. The bidders simultaneously submit bids b € [0, ∞), and whoever submits the higher bid wins the object and pays the average of the two bids. In case of a tie, each bidder wins the object with probability 1/2 and again the winner pays the average of the two bids. Find a Nash equilibrium of this game in which each bidder's strategy is linear in her valuation. Solution: Look for a symmetric equilibrium where each player bids according to b(v) = av+c. First note that in equilibrium, b(0) = 0 since otherwise types with valuations just above 0 win with positive probability and pay more than their valuation, and hence would prefer to lower their bids. Hence e=0. For every valuation vi for player 1, v₁ = ' must solve max Pr(b₂

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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