Asymmetric Auctions with Resale Isa Hafalir and Vijay Krishna (2008)
American Economic Review 98, 87-112.
(A brief summary. Presenter: Kohei Shiozawa)
Introduction (1/4) When do resale possibilities matter? •
An auction with inefficient allocations
(e.g., first-price with asymmetric bidders)
Why do resale possibilities matter? •
Virtually we can not prevent resale
(e.g., spectrum auction in UK in 2000)
•
Post auction resale results in efficiency?
(i.e., is an inefficient auction just as good?) 2 /18
Introduction (2/4) This paper •
Auctions with two asymmetric bidders
•
Only the winning bid is announced
•
Post auction trade (resale) is possible
•
Resale takes place via monopoly pricing
3 /18
Introduction (3/4) Main results •
Characterization of equilibrium of
the first-price auction with resale
•
Derivation of an equilibrium of
the second-price auction with resale
•
General Revenue ranking:
first-price second-price
4 /18
Introduction (4/4) Contributions •
Characterization of equilibrium of
the first-price auction with resale
Under asymmetry, characterization and
revenue results are few and far between. •
General Revenue ranking:
first-price second-price
Under asymmetry, it is well known that there
is no general revenue ranking without resale. 5 /18
First-price auction with resale (FPAR) Main assumptions •
Two asymmetric bidders
•
Assume that
and (FOSD)
The model 1. Bidders participate in a first-price auction. 2. The winning bid is publicly announced. 3. The winner can offer a resale price. 4. The looser can choose to accept it or not. 6 /18
First-price auction with resale (FPAR)
7 /18
First-price auction with resale (FPAR) A. Resale stage •
Suppose that bidder Bidder
•
If
wins with a bid of
would infer that bidder
offers a price
that solves
•
Let
denote the solution. 8 /18
First-price auction with resale (FPAR) B. Biding stage (1/4) •
Let
be equilibrium strategies.
•
Take any
•
Then, FOCs imply the following ODEs:
and let
be a bidder s.t.
9 /18
First-price auction with resale (FPAR) B. Biding stage (2/4)
Proposition 1. In equilibrium, the bid distributions
must be identical: Corollary 1. In equilibrium, bidder aggressively than bidder : 10 /18
bids more
First-price auction with resale (FPAR) B. Biding stage (3/4)
Observation: the FOC for the symmetric first-price
auction with some distribution is
11 /18
First-price auction with resale (FPAR) B. Biding stage (4/4) •
Let
be a distribution such that
•
Take the symmetric equilibrium a symmetric FPA with .
•
Define strategies as
of
constitute an equilibrium of FPAR. 12 /18
First-price auction with resale (FPAR)
Theorem 1. FPAR has an equilibrium in which
the bidding strategies are
Note that Expected revenues of FPAR and the symmetric FPA with are the same. 13 /18
Second-price auction with resale (SPAR) The model 1. Bidders participate in a second-price auction. 2. The winning bid is publicly announced. 3. The winner can offer a resale price. 4. The looser can choose to accept it or not. Remark The winner knows loser’s bid and hence value.
14 /18
Second-price auction with resale (SPAR) Proposition 2. SPAR has an equilibrium in which bidders bid their true value:
Resale Stage Winner is
believes that ’s type
offeres
iff
Bidding Stage If a bidder loses, his payoff is 0 truth-telling in SPA is never a bad action. 15 /18
Auctions with two asymmetric bidders. ⢠Only the winning bid is ... revenue results are few and far between. ... Observation: the FOC for the symmetric first-price.
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I identify conditions under which truthful communication by the decision maker fails in equilibrium and discuss the possibility of informative communication by the decision maker. Keywords: Two-sided asymmetric information, one-way communication, two
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Jan 17, 2009 - 0 > Vm t , and buying (or selling) is strictly preferred to other actions. Alessia Testa (University of Oxford). Herding with Asymmetric Information.
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Aug 26, 2009 - 1201 West University Drive, Edinburg, Texas 78539, USA, email: ... consider a model of a perfectly divisible good in which the marginal cost of the seller is known to the ..... If 0 ⤠xi ⤠xâi/2, it is not profitable for the sell
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The complete proof of Theorem 2 is rather technical, and is provided in Appendix B. To gain ..... auctions. Decision support systems, 43(1):192â198, 2007.