Transcript Slides

Probabilistic Asymmetric
Information and Lending
Relationships
Philip Ostromogolsky
Yale School of Management
Background
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Often banks lend to small business customers over
several periods.
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Banks may offer a customer a first-time loan with the
possibility that the customer may be able to get another,
future loan from the bank if he does a good job repaying
the first loan.
Over the period of the first loan the bank can
monitor his borrower, learn about him, and use that
information to extend or curtail future credit.
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More information than is revealed by simply observing
whether or not the customer repays his first-time loan.
How do banks compete over small
business borrowers?
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They bargain, just like stock brokers or
shoppers at a public market.
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This can be modeled as an English auction.
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Banks are the bidders.
The potential small business borrower is the
auctioneer.
A Simple Story About an Auction
A Simple Story About an Auction
?
A Simple Story About an Auction
I’m coming
back to the
White House
Bill
I’m coming
back to the
White House
What would Greenspan do?
Bill
Ben
A Simple Story About an Auction
V
 realized value of box's contents
bi*
 bidder i's highest bid
 i (bi* )  bidder i's profit given his highest bid = bi*
*
*
*

V

b
if
b

b
i
i
i
 i (bi* )  
*
*
0
if
b

b
i
i

A Simple Story About an Auction
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The auctioneer says:
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We will now conduct the auction, the highest bid ≥ 0 wins.
There is some probability p* [0,1] that the box contains a
$100 bill.
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I am not going to publicly disclose p*.
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But, I will tell you that p* ~U[0,1]
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I like Bill, so I am going to walk over to Bill and whisper in
his ear the value of p*.
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Ben is not going to be told anything about p*.
The auctioneer walks over to Bill and whispers the
value of p* into his ear.
A Simple Story About an Auction
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Bill is informed
Ben is uninformed
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Bill makes the first bid
Bill’s bid = $0.00
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What should Ben do?
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A Simple Story About an Auction
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Ben Thinks:
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Suppose probability that the box contains $100 = p* = 0.5,
and of course Bill knows this.
Bill knows that the expected value of the box’s contents
= 100p* = 50.
Bill will continue bidding up until Bill’s bid = 50.
If at some point Bill bids 50 and I then bid 51, I will win.
When the auctioneer announces that I have won my
expected profit will
= 100p* – my bid = 100*0.5 – 51 = 50 – 51 = -1.
So, when I am announced as the winner I will expect to
have a profit of -1 < 0.
A Simple Story About an Auction
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Ben Thinks:
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If at some point I (Ben) bid 50, I will win.
When the auctioneer announces that I have won my
expected profit will
= 100p* – my bid = 100*0.5 – 50 = 50 – 50 = 0.
So, when I am announced as the winner I will expect to
have a profit of 0.
If I ever bid some bid, Ben’s bid < 50, I of course will not
win.
Thus, if p* = 50 and I don’t know that, I can never win, and
I might actually lose!!!
A Simple Story About an Auction
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Ben Thinks:
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As of right now, the last bid, was Bill’s bid = 0.
I don’t actually know p*.
The lowest I could bid is $1.
If p* > 0.01 then the best I could hope for would be go get a
profit of π = 0.
If p* < 0.01, then my profit would =
π = 100p* – 1 < 100*0.01 – 1 < 0
And, I would lose money!!!
Pr(p* < 0.01) = 0.01.
So, if I bid $1, the expected value of my profits =
E[π] = 0.01(100p* - 1) = p* - 0.01 < 0 !!!
A Simple Story About an Auction
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Thus, Ben drops out of the auction
and Bill obtains the contents of the box for a
winning bid of $0.
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Bill’s interim expected profits from this game are
thus
E[π|p*] = 100p* – 0 = 100p*
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Bill’s ex ante expected profits from this game are
Ep*[E[π|p*]] = 100E[p*]– 0 = 50.
A Simple Story About an Auction
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Bill’s knowledge of p* does not just let him
make a more accurate forecast of the
expected value of the contents of the box.
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this is an old idea.
It also gives him a credible deterrence
device, through which he can force his
opponent to exit the auction, and ensure
himself maximum possible profits.
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this is new idea.
The Experiment
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4 Simultaneous Auctions run by Boudhayan, Foong
Soon, Michael, and me.
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Each auction had 3 bidders.
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Selection of informed bidder, randomization of p*
and realization of box contents performed using
random draws of poker chips.
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Induce risk neutrality by giving each student an
initial endowment of 10,000 point.
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Incentivize strategic behavior by offering prizes for
the 3 students having the most aggregate profit.
Results – Looks Good 
Results – Some Participants Seem
Almost Risk Loving 
Results
Table 1. Auctions Won By Informed and Uninformed Bidders
Number of
Proportion of All
Auctions Won
Auctions Won
Bidder
informed
11
0.33
uninformed
22
0.67
Table 2. Statistics About Winning Bids
mean
min
49.30
16
max
92
Results
Table 3. Profits Among Informed and Uninformed Bidders
All Auctions Auction # ≥ 5 Auction # ≥ 6 Auction # ≥ 7
47.00
47.00
27.00
44.45
informed
-27.67
-15.40
-20.64
-2.19
uninformed
mean π
informed –
74.67***
62.40***
47.64**
46.65***
uninformed
13.67
13.67
22.83
19.45
informed
-13.78
-11.23
-10.79
-4.17
uninformed
mean E[π |p* ]
informed –
27.44***
24.90***
33.62***
23.63***
uninformed
0.00
0.00
0.00
0.09
informed
Probability of uninformed
1.00
0.90
0.91
0.73
Overbidding informed –
-1.00***
-0.90***
-0.91***
-0.64***
uninformed