TY - JOUR

T1 - On the properties of equilibria in private value divisible good auctions with constrained bidding

AU - Kastl, Jakub

N1 - Funding Information:
The author is deeply indebted to my advisor Michael Whinston for his encouragement and invaluable comments. The author would also like to thank Jeff Ely, Ilan Kremer, Alessandro Pavan, Salvatore Piccolo, Robert Porter, Andy Skrzypacz, Tomasz Strzalecki, Bob Wilson, Asher Wolinsky, two anonymous referees and the co-editor for helpful comments. Financial support from the Center for the Study of Industrial Organization at Northwestern University and the NSF ( SES-0752860 ) is gratefully acknowledged. Any remaining errors are my own responsibility.

PY - 2012/12

Y1 - 2012/12

N2 - 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.

AB - 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.

KW - Discriminatory auction

KW - Multiunit auctions

KW - Step functions

KW - Uniform price auction

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U2 - 10.1016/j.jmateco.2012.07.006

DO - 10.1016/j.jmateco.2012.07.006

M3 - Article

AN - SCOPUS:84867898453

VL - 48

SP - 339

EP - 352

JO - Journal of Mathematical Economics

JF - Journal of Mathematical Economics

SN - 0304-4068

IS - 6

ER -