On the properties of equilibria in private value divisible good auctions with constrained bidding

Jakub Kastl

Journal of Mathematical Economics, 2012, vol. 48, issue 6, 339-352

Abstract: I analyze a model of a private value divisible good auction with different payment rules, standard rationing rule pro-rata on-the-margin and both with and without a restriction on the number of bids (steps) bidders can submit. I provide characterization of equilibrium bidding strategies in a model with restricted strategy sets and I show that these equilibria converge to an equilibrium of the model with unrestricted strategy sets as the restrictions are relaxed. However, not all equilibria in the unrestricted game can be achieved as limits of the equilibria of the restricted games. I demonstrate that the equilibrium conditions require that the Euler condition characterizing equilibrium in continuously differentiable strategies in the unrestricted model holds “on average” over the intervals defined by the length of each (price) step of the restricted strategy, where the average is taken with respect to the endogenous distribution of the market clearing price. The characterization from the restricted model also allows for a natural interpretation of the involved trade-offs. Adapting the argument of Chao and Wilson (1987) I also prove that the foregone surplus of a bidder from using K steps rather than a continuous bid is proportional to 1K2.

Keywords: Multiunit auctions; Uniform price auction; Discriminatory auction; Step functions (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (45)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304406812000572
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:48:y:2012:i:6:p:339-352

DOI: 10.1016/j.jmateco.2012.07.006

Access Statistics for this article

Journal of Mathematical Economics is currently edited by Atsushi (A.) Kajii

More articles in Journal of Mathematical Economics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().