Liz DiMascioPaige Warren-ShrinerMitch Justus

DUTCH AND ENGLISH AUCTIONS IN

RELATION TO THE TULIP MARKET

High initial starting price—price lowers until acceptable to a bidder

Strategically equivalent to fi rst-price sealed bid auctions

Dutch flower auction takes place every weekday in Aalsmeer, Netherlands

Retail flower salesman are participants

Frequently used in auctions for nondurable non-consumer goods

DUTCH AUCTIONS

Sequential

Bidders are purchasing goods for resale

Identical goods, identical bidders

Same number of goods each round

Independent Private Values (IPV): has a diff erent value for each bidder (= Revenue – IP Cost)

TYPICAL FEATURES OF NONDURABLE GOODS AUCTIONS

“Why Do We Use the Dutch Auction to Sell Flowers? —Information Disclosure in Sequential Auctions” (Tu)

Given several simplifying assumptions, Dutch auction with only winning bid announced produces higher revenue than English auction in a sequential environment

PRIVATE VALUE LITERATURE

Bidders bid symmetrically according to bid function B(v)

In second round, winner believes that loser’s value lies in interval [0,v) where v is winner’s value

Loser calculates second bid based on fi rst, losing bidB(v) for fi rst round = v/2First stage winner randomizes over (v/2, 3v/4)Loser will not bid if v < v’/4, where v’ is inferred

valuation of fi rst stage winner In second stage, winner and loser are brought to

relatively level playing ground (since loser of fi rst round has informational advantage, while winner randomizes)

DUTCH AUCTION WITH WINNER’S BID REVEALED

Common Value Good: has one true underlying value for all bidders. This value is unknown at the time the bid is placed, and bidders receive independent signals of it. Values are infl uenced by others’ signals.

Private Value Good: has a diff erent value for each bidder Usually used to describe modern day auctions of

nondurable non-consumer goods

PRIVATE VALUE VS. COMMON VALUE

“A Theory and Auctions and Competitive Bidding” (Milgrom, Weber) Consideration of revenue in static auctions (non-sequential)

Common Value Auctions and the Winner’s Curse (Kagel, Levin)

COMMON VALUE LITERATURE

1630s: Tulip market in Amsterdam undergoes widespread speculation leading to a price bubble

Professional growers and nonprofessional speculators interested in resale value of tulips (experienced bidders)

Tulips in the 1630s were common-value goods, not private value (because of local nature of market, costs were more or less equivalent, and revenue, a common-value derived from aggregate demand, was unknown)

Each bidder receives a “signal” of market demand of certain tulips This market demand is the true resale value of the tulips to each

bidder

TULIPS IN THE 1630’S

What conclusions can be drawn from sequential auctions for common value goods, such as those that took place for tulip bulbs in the 1630’s?

Bidding strategies Information asymmetrySeller’s revenues

OUR QUESTION

2 participants, 2 auction rounds, 2 identical goods (with one being auctioned each round)

True value of good is unknown at the time each player submits their bid, and is drawn from a discrete distribution of 5 consecutive integers The true value of the goods are unique to each competing

pair

Each player receives a private signal of the value of the good Each player’s signal is drawn from the same distribution as

the true value of the good, thus, a player’s signal will be no more than 2 units away from true value of the good

OUR EXPERIMENT

High starting price will be announced, then begin descending by one

Each bidder’s profi t = True value of good – Bid (Profi t = 0 for loser)

First bidder among each competing pair to bid wins auction

Ties will be randomly broken

Each player will record their signal, bid in each round, whether they won or lost, and the true value of the good (given after the second round)

AUCTION 1: DUTCH AUCTION

PROBABILITY DISTRIBUTION OF SIGNALS, GIVEN TRUE VALUE OF

GOOD = 3

Price will start from 1, all bidders willing to purchase the good at a price = 1 will indicate their willingness to bid at this price

Price will ascend by an increment of 1 until one bidder (in each competing pair) drops out

Profi t = True Value of Good – Price at which previous bidder dropped out

Same relationship between signals and true values of goods holds

Each player will record their signal, bid in each round, whether they won or lost, and the true value of the good (given after the second round)

AUCTION 2: ENGLISH AUCTION

2 bidders, 2 rounds

Symmetric strategies

Same true value both rounds

Signals randomly drawn from discrete distribution made to approximate a normal distribution

Dutch auction, winner’s bid becomes known

Experienced bidders (eliminates winner’s curse)

OUR MODEL

ASSOCIATED PROBABILITIES OF SIGNALS AND AUCTION RESULTS

PROFIT FROM USING GIVEN STRATEGY

PROFIT FROM USING GIVEN STRATEGY

PROFIT FROM USING GIVEN STRATEGY

PROFIT FROM USING GIVEN STRATEGY

PROFIT FROM USING GIVEN STRATEGY

NEW VALUATIONS

SECOND ROUND STRATEGIES

What about the continuous normal distribution?

Can’t fully eradicate winner’s curse (unbounded distribution).

What about the English Auction?

What is the optimal bidding strategy in the first round?

How valuable is information about the other bidder’s signal

Is it necessary to use a model with >2 bidders?

Revenue

What is the exact relation between bidders’ auction format and seller’s revenue?

PLANNED EXTENSIONS

Kagel, John H., and Dan Levin. Common Value Auctions and the Winner’s Curse. Princeton: Princeton University Press, 2002. eBook.

Milgrom, Paul R. and Robert J. Weber (1982); “A Theory of Auctions and Competitive Bidding,” Econometrica, 50, 1089-1122.

Tu, Zhiyong. Why Do We Use the Dutch Auction to Sell Flowers? – Information Disclosure in Sequential Auctions. Diss. The University of Pittsburgh, 2006. Web.

REFERENCES