Determinants of Aggressive Bidding in the “Buying a Company” Task

Andy Lockett - School of Business, University of Nottingham

Elke Renner - School of Economics, University of Nottingham

Martin Sefton - School of Economics, University of Nottingham

Deniz Ucbasaran - School of Business, University of Nottingham

Winner’s Curse

In general, when bidding for an object of unknown value the person

who most overestimates true value most likely to be winner …

Winning bidder often makes expected losses

Auctions (e.g. Oil field drilling rights)

Acquisitions

Start-ups

Buying a Company(Samuelson and Bazerman, 1985)

Company worth v to current owner and 3v/2 to potential buyer

v uniformly distributed on [0, 100], observed by owner

Potential buyer makes bid, b

Current owner accepts Owner receives b - v

Buyer receives 3v/2 - b

or rejects Owner receives 0

Buyer receives 0

Optimal bid

Owner: accepts if b v, rejects otherwise

Buyer: expected profit = E[3v/2 – b|b v] Pr{b v}

Optimal bid: b* = 0

Samuelson and Bazerman (Research in Experimental Economics, 1985). Subjects generally bid between E(v) = 50 and E(3v/2) = 75.

Ball, Bazerman and Carroll (Organizational Behavior and Human Decision Processes, 1991). Learning from own outcome over multiple trials does not reduce winner’s curse.

Holt and Sherman (American Economic Review, 1994). Vary distribution of v and find data consistent with a model of naiive bidding: maximize E[3v/2 – b] Pr{b v}.

Charness and Levin (2005). Frame task as an individual decision problem, vary complexity of distribution of v, measure mathematical sophistication. Winner’s Curse survives, is lower with less complex distributions, lower for more mathematically sophisticated.

Experimental Evidence

Selten, Abbink and Cox (Experimental Economics, 2005):

Frame task as individual decision problem, vary lower bound of uniform distribution (u), focus on learning.

Experimental Evidence

Goal of this experiment

1. Can winner’s curse be reduced by learning from others?

We compare bids made by individuals with bids made by pairs who can discuss problem

We study effect of giving bidders information about others’ outcomes

2. How are bids related to individual characteristics?

We elicit risk attitudes, measure mathematical sophistication, demographic data.

The Experiment

178 Subjects from University of Nottingham School of Business

Each Session: Buying a Company

Eliciting Risk Attitudes

Assessing Probabilities

Questionnaire

4 Sessions: INDIVIDUAL: 27 subjects

TEAM: 25 x 2 subjects

INDIVIDUAL + INFO: 39 subjects

TEAM + INFO: 31 x 2 subjects

Average earnings £ 17.55 for sessions lasting approx. one hour

PART ONE: ACQUIRING A COMPANY

Task A

The basic decision

Your task is to submit a bid for a company.

You have an initial endowment of 100 points which you can use to bid for the company,i.e. your bid can be any number between 0 and 100 points.

The value of the company

The current owners of the company know the exact value of the company to them. Whenyou decide what to bid, you will not know what this value is. However, you know threethings:

1. The value of the company to the current owner is equally likely to be anynumber of points between 1 and 99.

2. You will acquire the company if your bid is greater than or equal to the value ofthe company to the current owners.

3. The value of the company to you is 1½ times the value of the company to itscurrent owners.

Your point earnings

If you do not acquire the company (i.e. your bid is lower than the value of the companyto its current owners):

Your point earnings = 100

If you do acquire the company (i.e. your bid is greater than or equal to the value of thecompany to its current owners):

Your point earnings = 100 – Your bid + Value of the company to you

Procedures

You must decide on your bid, enter it at the bottom of this page.

The value of the company to the current owners will be determined at the end of theexperiment by the following procedure:

You will draw a numbered chip from a bag that contains chips numbered from 1 to 99.The value of the company to the current owners will be equal to the number you draw.The value of the company to you will be 1½ times the number you draw.

Enter your bid:______________ points

Notes:

This is one of the parameterizations used in Selten, Abbink, Cox (2005)

We also had subjects make decisions for their other parameterizations:

Task B (same as A but chips 11-99)

Task C (same, but chips 21-99)

Task A: optimal bid = 1

Task B: optimal bid = 22

Task C: optimal bid = 42

All three tasks played out at end of experiment

TaskLottery

Your choicePlease check one of thetwo circles for each task

Sure Payoff

A£5 with probability ½,

£0 with probability ½? ? £0.50

B£5 with probability ½,

£0 with probability ½? ? £1

C£5 with probability ½,

£0 with probability ½? ? £1.50

D£5 with probability ½,

£0 with probability ½

? ? £2

E£5 with probability ½,

£0 with probability ½? ? £2.50

F£5 with probability ½,

£0 with probability ½? ? £3

G£5 with probability ½,

£0 with probability ½? ? £3.50

H£5 with probability ½,

£0 with probability ½

? ? £4

I£5 with probability ½,

£0 with probability ½? ? £4.50

PART TWO: MAKING A RISKY CHOICE

Notes:

This is similar to risk elicitation procedure used in Dohmen, Falk, Huffman, Sunde, Schupp and Wagner (2005)

Switching point gives measure of risk attitude

Switching point = amount up to which subject chooses lottery

(e.g. 2.5 means subject chose lottery when safe option is 2.5 or less, then chooses safe option when safe option 3 or more)

010

2030

0 .5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 .5 1 1.5 2 2.5 3 3.5 4 4.5 5

INDIVIDUAL TEAM

Fre

qu

en

cy

Switching Point

No significant difference between INDIVIDUAL and TEAM (p=0.559)

68 risk averse decisions, 47 consistent with risk neutrality (2.5 or 3), 4 risk loving

decisions, 3 inconsistent decisions (not shown)

Based on INDIVIDUAL data:

Male (n = 49) average switchpoint = 2.21

Female (n = 17) average switchpoint = 1.74

Women more risk averse than men (Fisher exact test: p = 0.026)

PART THREE: ASSESSING PROBABILITIES

Consider two machines placed on two sides of a large production hall, the left machineand the right machine. The two machines produce rings, good ones and bad ones.

Each ring that comes from the left machine has a 50% chance of being a good ring and a50% chance of being a bad ring.

Each ring that comes from the right machine has a 75% chance of being a good ring and a25% chance of being a bad ring.

In each of the following 4 questions you will observe some ring(s) that are the output ofone of the two machines. After the information is given, you are asked to mark one (andonly one) of the probabilities that you think is closest to the true probability that the leftmachine produced the ring(s), given your observations.

At the end of the experiment you will be paid £0.50 for each correct answer.

Q1. You observe one good ring. What is your best assessment of the probability that theleft machine produced this ring?

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

? ? ? ? ? ? ? ? ? ? ?Q2. You observe one bad ring. What is your best assessment of the probability that theleft machine produced this ring?

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

? ? ? ? ? ? ? ? ? ? ?Q3. You observe six rings, and all six are bad. What is your best assessment of theprobability that the left machine produced these rings?

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

? ? ? ? ? ? ? ? ? ? ?Q4. You observe six rings, of which three are good and three are bad. What is yourbest assessment of the probability that the left machine produced these rings?

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

? ? ? ? ? ? ? ? ? ? ?

Notes: This is same as used in Charness and Levin (2005)

010

2030

0 1 2 3 4 0 1 2 3 4

INDIVIDUAL TEAM

Fre

quen

cy

# correct (part III)

Significant difference between INDIVIDUAL and TEAM (p=0.007)

Based on INDIVIDUAL data, males score higher than females (1 vs. 0.59) but difference marginally significant (p = 0.13)

Histograms of Bids: INDIVIDUAL (n=27)

Task A

Task B

0

1

2

3

4

5

6

0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-99

Freq

uen

cy

av = 40s.d. = 26

0

1

2

3

4

5

6

7

8

0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-99

Freq

uen

cy

av = 45s.d. = 21

0

1

2

3

4

5

6

7

8

0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-99

Freq

uen

cy

Task C

av = 57s.d. = 20

Statistical Comparisons

1. Bids increase significantly across tasks as predicted: bidA < bidB (signrank p =0.001)

bidB < bidC (p=0.000)

2. Significant over-bidding. Median bid significantly above predicted bid: Median Bid A = 40 (signtest p=0.000)

Bid B = 45 (p=0.000)

Bid C = 58 (p=0.001)

0

1

2

3

4

5

6

7

8

0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-99

Freq

uen

cy

Histograms of Bids: TEAM

Task A

Task B

0

1

2

3

4

5

6

7

0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-99

Freq

uen

cy

av = 37s.d. = 20

Task C

av = 44s.d. = 20

0

1

2

3

4

5

6

0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-99

Freq

uen

cy

av = 53s.d. = 21

Histograms of Bids: TEAM (n=25)

Statistical Comparisons

1. Bids increase significantly across tasks as predicted: bidA < bidB (signrank p =0.000)

bidB < bidC (p=0.000)

2. Significant over-bidding. Median bid significantly above predicted bid: Median Bid A = 37 (signtest p=0.000)

Bid B = 48 (p=0.001)

Bid C = 53 (p=0.011)

3. No significant differences between INDIVIDUAL and TEAM: Bid A: INDIVIDUAL = TEAM (ranksum p=0.8185)

Bid B: INDIVIDUAL = TEAM (p=0.9051)

Bid C: INDIVIDUAL = TEAM (p=0.3540)

+ INFO Sessions

Subjects given selective information from earlier sessions:

INDIVIDUAL + INFO: 19 subjects given negative information, 20 given

positive information

TEAM + INFO: 15 teams given negative information, 16 given positive

information

Positive InformationAdditional Information

An experiment was conducted earlier this week, with participants who signed up in the same way as you. Fifty-two participants submitted bids for these same tasks. Some of the bids resulted in point earnings above 100. These bids and the resulting point earnings are listed below for each task:

Task A Task B Task C

Bid Point

earnings

Bid Point

earnings

Bid Point

earnings 35 102.5 11 105.5 39 107.5 50 120.5 15 106 40 100.5 50 123.5 30 103 45 113.5 51 119.5 30 109 47 116 80 119 40 103.5 50 111.5 99 140.5 50 119 55 106.5

55 121.5 55 123 55 123 60 110.5 60 115 60 115 60 122.5 65 102.5 65 114.5 67 133.5 70 121.5 80 107 70 126 80 108.5 75 136 90 115 90 142

Negative InformationAdditional Information

An experiment was conducted earlier this week, with participants who signed up in the same way as you. Fifty-two participants submitted bids for these same tasks. Some of the bids resulted in point earnings below 100. These bids and the resulting point earnings are listed below for each task:

Task A Task B Task C

Bid Point

earnings

Bid Point

earnings

Bid Point

earnings 25 78 40 84 40 94.5 30 80.5 55 73.5 50 92 30 83.5 62 63.5 50 95 30 85 77 74 56 86 45 65.5 80 68 58 79.5 45 70 82.5 38.5 65 92 48 71.5 67 79.5 50 62 70 84 50 62 70 91.5 51 55 70 94.5 55 67.5 80 57.5 57 64 84 86.5 60 49 99 50.5 60 59.5 70 90 75 85

Summary of Bids

Means and Standard DeviationsBid A Bid B Bid C

NOINFO

40 (26) 45 (21) 57 (20)

NEGATIVEINFO

46 (27) 52 (21) 52 (18)INDIVIDUAL

POSITIVEINFO

45 (24) 51 (22) 59 (24)

NOINFO

37 (20) 44 (20) 53 (21)

NEGATIVEINFO

48 (21) 51 (16) 67 (11)TEAM

POSITIVEINFO

42 (24) 53 (17) 63 (18)

ALL 42 (24) 49 (20) 58 (20)

Statistical Comparisons

INDIVIDUAL: No statistical effect: bidA (Kruskal-Wallis p =0.590), bidB (p = 0.491), bidC (p=0.274)

TEAM: only bid C significantly differs across information conditions: bidA (p = 0.264), bidB (p = 0.346), bidC (p = 0.038)

bid C: negative info leads to higher bid than no info

Determinants of Bids - INDIVIDUALS

Dependant Variable

Bid A Bid B Bid C

Cons 32.21*** (10.90) 30.89*** (9.13) 50.82*** (9.37)

PosInfo 7.92 (7.44) 7.32 (6.23) -4.57 (6.40)

NegInfo 6.91 (7.31) 7.10 (6.12) 2.81 (6.29)

RISK 2.81 (4.19) 6.34* (3.51) 2.07 (3.60)

MATH -4.56 (3.24) -2.97 (2.73) 0.01 (2.80)

FEMALE 18.23** (7.38) 12.68** (6.18) 5.86 (6.34)

Preliminary Conclusions

Robust Winner’s Curse – individuals systematically overbid

Two Heads not Better than One – teams make statistically

indistinguishable bids

No Information effect – individuals not affected by pos/neg info

Risk attitudes have small and insignificant effect on bids

Mathematical sophistication has small and insignificant effect on bids

Females bid more aggressively