The Winner’s Curse

Table of Contents• 1. Introduction – The Theory of Winner’s Curse. How does one

define the Winner’s Curse?

• 2. Context - What are some real world examples of this anomaly?

• 3. Existing Literature – What are some samples of published books and papers on the subject?

• 4. Review – 3.5 minute video. A salient example to illustrate the type of losses this anomaly is responsible for.

Theory of Winner’s Curse• Approximately, there are 3 categories of auctions• In a private value auction, individuals’ values for the object being auctioned are

determined independently of each other. So, knowing my own private value signals nothing about the value of the object to others.

• In a common value auction, the object is identical in value for all bidders. Thus, the visible signal of varying bids arises from differences of opinion about what the true value of the object actually is.

• An affiliated value auction is somewhere between a private value and a common value auction. While the value of the item being auctioned is different for each bidder, these values are positively correlated among bidders. Thus, knowing my own value signals something about the value of the item for other bidders. In reality, most auctions fall under this categeory.

Simple Model of a Winner’s Curse

• 3 individuals are bidding for a picture.• Incomplete information sealed-price first bid auction, where

only one bid per person and bids are made independently• Picture is appraised in an auction setting at $9 million.• Let T = bid amount in this example.• Bid Probability this is the winning bid• T = 8 = 1/3 * 1/3 * 1/3 = 1/27• = 3.7%• T = 9 = 1 – .037 – .704 = 7/27• = 25.9%• T = 10 = 1- 2/3 * 2/3 * 2/3 = 19/27• = 70.4%

Simple Model of a Winner’s Curse

• E(winning bid) = $9.667 million > $9 million.• In more than 70% of the time the winner of the auction

pays more than the picture is worth.

Real World examples• Oil drilling • At the start of the 1940’s, oil companies began the race to

secure drilling rights.• By 1960, despite many offshore wells were already in

production, it became common knowledge that this business was unprofitable.

• Based on three ARCO employees research, estimates found in ARCO’s oil-drilling bidding history would sometimes differ tenfold between two bidders competing for the same site.

Other examples• Governments auction (3G) mobile telecommunication

spectrums, CO2 permits, and defense contracts.

• (IPOs) are also an example, since bidders need to estimate what the market value of a company stock will be.

• Internet business auction websites, such as E-bay, are a significant example of a common occurrence of the winner’s curse .

Existing Literature• "The Winner's Curse: Paradoxes and Anomalies of Economic

Life" by Richard H Thaler

• The winner’s curse occupies one relatively short chapter in the book. There are the familiar examples of auctions of jars of coins, and the seminal paper on the bidding for oil-field drilling rights (Capen, Clapp & Campbell. 1971), which first coined the phrase “Winner’s Curse”.

Existing Literature• Kagel & Levin: “The Winner’s Curse and Public Information in

Common Value Auctions”• Does experience with first price common value auctions

reduce occurrence of the winner’s curse? • If experience does reduce overbidding, can we say something

about what subjects are learning? • The theory suggests that a larger correction for the winner’s

curse is needed in settings where the number of bidders is large.

Kagel & Levin (Continued)

• For all of the auctions in this paper, the value x was distributed uniformly over a range [-x,+x] that was common knowledge. After x is drawn, each subject then receives a signal about the value that is distributed uniformly over the interval [x – ε, x+ε]. The value of ε is commonly known to all bidders.

• Below is the risk neutral nash equilibrium bid function. The final term goes to zero rapidly as we depart the lower end of the distribution, so normally a bidder should bid only slightly above the minimum possible value of the object’s signal.

Existing Literature• “The winner's curse with independent private values.” by

Olivier Compte• This paper challenges the view that the winner’s curse

anomaly is attributed only to common value or affiliated value auctions.

• Uniquely, this author uses the approach introduced by Capen and al. (1971) and extends this insight to independent private value settings where costs are drawn from independent distributions and where bidders have imperfect estimates of their own valuation.

Too early to confirm example

Corporate Olympics

Olympic Games!• http://www.cbc.ca/video/watch/Embedded-Only/News/

ID=2261856745

Olympic Costs

Ballooning Costs• Olympic security costs

• 2012 London – $1.6 billion• 2010 Vancouver – $1 billion• 2008 Beijing – $6.5 billion (estimated)• 2006 Turin – $1.4 billion• 2004 Athens – $1.5 billion• 2002 Salt Lake City – $500 million• 2000 Sydney – $180 million

• *all in US $

‘Overconfidence’(Moore and Healy, 2008)

• Overestimation: “overestimation of one’s actual ability, performance, level of control, or chance of success.”

• Overplacement: “people believe themselves to be better than others, such as when a majority of people rate themselves better than the median.”

• Overprecision: “excessive certainty regarding the accuracy of one’s beliefs”

Social Image (Ariely et al., 2009)

• Hypotheses derived from Benabou and Tirole (2006) (see also McConnell and Linardi, 2011)

• Image Motivation Hypothesis—Ceteris paribus, changing ‐visibility changes the level of prosocial activity. For a positive image, increasing visibility increases the level of prosocial activity.

• Effectiveness Hypothesis—Extrinsic rewards are less effective the greater is the visibility of the prosocial act.