Consider a variant of the sealed-bid auctions with imperfect information considered in class in which the...
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Consider a variant of the sealed-bid auctions with imperfect information considered in class in which the players are risk-averse. Specifically, assume that the payoff of a player with valuation v who wins the object and pays the price p is (v- p)1/m, where m > 1. (In class we considered the case m 1, in which the bidders are "risk neutral". For m > 1, the bidders are "risk averse".) 1. [7 points] Find an equilibrium of the second-price auction. 2. [12 points] Suppose that there are two players and each player's valuation is drawn independently from a uniform distribution on [0, 1] (as we assumed in class). Find an equilibrium of the first- price auction. (Hint: Assume that the player strategy is a linear function of their evaluation, i.e. when player 2's valuation is v2 she bids Bv2, where B is a constant. Find the best response of player 1 to this strategy of player 2 when player l's valuation is v1.) 3. [6 points Following the environment of part (2) (two players, uniform distribution of valuations), compare the expected value of the price paid by a winner with valuation v in the equilibrium of a second-price and a first-price auction. How does the auctioneer's revenue differ between the two auctions?. Consider a variant of the sealed-bid auctions with imperfect information considered in class in which the players are risk-averse. Specifically, assume that the payoff of a player with valuation v who wins the object and pays the price p is (v- p)1/m, where m > 1. (In class we considered the case m 1, in which the bidders are "risk neutral". For m > 1, the bidders are "risk averse".) 1. [7 points] Find an equilibrium of the second-price auction. 2. [12 points] Suppose that there are two players and each player's valuation is drawn independently from a uniform distribution on [0, 1] (as we assumed in class). Find an equilibrium of the first- price auction. (Hint: Assume that the player strategy is a linear function of their evaluation, i.e. when player 2's valuation is v2 she bids Bv2, where B is a constant. Find the best response of player 1 to this strategy of player 2 when player l's valuation is v1.) 3. [6 points Following the environment of part (2) (two players, uniform distribution of valuations), compare the expected value of the price paid by a winner with valuation v in the equilibrium of a second-price and a first-price auction. How does the auctioneer's revenue differ between the two auctions?.
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1 In a secondprice auction with riskaverse bidders the equilibrium is for each player to bid their t... View the full answer
Related Book For
Modeling the Dynamics of Life Calculus and Probability for Life Scientists
ISBN: 978-0840064189
3rd edition
Authors: Frederick R. Adler
Posted Date:
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