English auctions with ensuing risks and heterogeneous bidders

We establish conditions under which an English auction for an indivisible risky asset has an efficient ex post equilibrium when the bidders are heterogeneous in both their exposures to, and their attitudes toward, the ensuing risk the asset will generate for the winning bidder. Each bidder’s private...

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Bibliographic Details
Published in:Journal of mathematical economics 2018-05, Vol.76, p.33-44
Main Authors: Hu, Audrey, Matthews, Steven A., Zou, Liang
Format: Article
Language:English
Subjects:
Assets
Attitudes
Auctions
Bidders
Bids
English auction
Ensuing risk
Equilibrium
Ex post efficiency
Ex post equilibrium
Expected values
Heterogeneous risk preferences
Interdependent values
Mapping
Marginal utility
Risk
Risk aversion
Willingness to pay
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Summary:We establish conditions under which an English auction for an indivisible risky asset has an efficient ex post equilibrium when the bidders are heterogeneous in both their exposures to, and their attitudes toward, the ensuing risk the asset will generate for the winning bidder. Each bidder’s privately known type may affect both his risk attitude and the expected value of the asset’s return to the winner. An ex post equilibrium in which the winning bidder has the largest willingness to pay for the asset exists if two conditions hold: each bidder’s marginal utility of income is log-supermodular, and the vector-valued function mapping the type vector into the bidders’ expected values for the asset satisfies a weighted average crossing condition. However, this equilibrium need not be efficient. We show that it is efficient if each bidder’s expected value for the asset is nonincreasing in the types of the other bidders, or if the bidders exhibit nonincreasing absolute risk aversion, or if the asset is riskless.
ISSN:0304-4068
1873-1538
DOI:10.1016/j.jmateco.2018.02.002