Applying Game Theory to Finance
“I can calculate the motions of
heavenly bodies, but not the
madness of people”
- Isaac Newton, upon losing £20,000 in the
South Sea Bubble in 1720
Game Plan

Hostile Takeovers

Bubbles
David McAdams
2
Hostile Takeovers
“Robert Campeau is considered by
many as the best example of a fool.”
- Dale Oesterle, Cato Review of Business & Government, 1996
“The biggest, looniest deal ever."
- Fortune Magazine, July 1988, on Campeau’s acquisition of Federated Stores.
Hostile Takeover Plan

Robert Campeau vs. Macy’s for Federated
• Conditional vs. unconditional offers
• Flat vs. tiered offers

Qwest Bond Swap
• Coercive offers
• Staggered offers

Poison Pills, Saturday Night Specials, etc.
David McAdams
4
Macy’s vs. Campeau

You are shareholders of Federated,
whose share price is $100.

Macy’s offers you $105 per share
conditional on getting at least 50%

Campeau offers an unconditional
tiered offer …
David McAdams
5
Macy’s vs. Campeau


If less than 50% tender to him, then each
gets $110 per share.
If X% > 50% tender to him, then each
gets a “blended price” of
50% * $110  ( X  50)% * $80
• Campeau pays $80 extra per share beyond 50%
• If everyone tenders, Campeau pays $95 per share
• If Campeau wins and you have not tendered, then
Campeau will be able to buy you out at $80
David McAdams
6
Macy’s vs. Campeau
Do you:
Tender to Macy’s
OR
Tender to Campeau?
David McAdams
7
Qwest Bond Swap
“Today a federal judge will decide whether
Qwest can proceed with an exchange
offer in which institutional investors (in a
$1.5B issue) are being asked to exchange
each $1,000 bond for a new one with face
value $545. The offer is a coercive one
that will leave bondholders who do not
accept it in the back of line for repayment
if Qwest goes broke…”
- “A Bond Swap Available Only to Big Players”, NY Times, December 18,
2002.
David McAdams
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Qwest Bond Swap
“If Judge Chin allows the offer to go
ahead, institutional investors who own
bonds will find themselves in a position
with some resemblance to the classic
‘prisoners’ dilemma’... If no one tendered,
then Qwest would be in the same position
as before the offer, and any bondholder
would be no worse off. But if a lot of
holders tender, those who refuse will be
worse off than they were.”
- “A Bond Swap Available Only to Big Players”, NY Times, December 18,
2002.
David McAdams
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Qwest Coercive Bond Swap

How is / is not the game played
among bondholders similar to the
Prisoners’ Dilemma?

Why exclude non-institutional
investors from the offer?
David McAdams
10
Qwest: Some Simple Cases

Qwest owes $1.5B w/ $600M assets.
• Given success (everyone tenders) Qwest still goes
bankrupt
• Is it a dominant strategy to tender?

Qwest owes $1.5B w/ $1B assets
• Given success, Qwest avoids bankruptcy
• Is it a dominant strategy to tender?
David McAdams
11
Qwest: Less Simple Cases

Qwest owes $1.5B w/ assets that are
worth either $600M or $1B.
• Given success, it avoids bankruptcy w/
Prob($1B)=45%
• Is tender a dominant strategy here?
• … for higher or lower Prob($1B)?

Same as above but $300M worth of
bondholders are excluded from the deal
• Tender becomes a dominant strategy for the $1.2B
who remain
David McAdams
12
Qwest Continued: When All
Bonds aren’t Created Equal


In reality, Qwest had many different bond
issues it wanted to retire through these
swaps, with different repayment priority.
Qwest also didn’t issue its swap offers for
all of its issues at once but rather
staggered the offers
Does the order matter?
Should Qwest swap high-priority bonds
first or low-priority ones?
David McAdams
13
Zwest Game

Fictional firm Zwest has three
bondholders A,B,C each owed $3M.

There is some uncertainty about Zwest’s
future assets: Zwest will have $5 million
with 66.7% and $8 million with 33.3%.

Absent any tendering, A gets repaid first
followed by B, then C.
• Since assets are always less than $9 million, Zwest
always goes bankrupt and has equity value of $0.
David McAdams
14
Zwest Game

Zwest will offer A,B,C each to exchange
their $3M bond for a priority $2M bond.

Those who tender will have higher priority
than those who don’t, but priority
rankings are preserved between those
that tender and those that don’t.
• Example: if only B tenders, then B is paid $2M first
then A is paid $3M then C is paid either $0M or $3M,
depending on whether asset value is $5M or $8M.
David McAdams
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Zwest Game #1 (A first)

Zwest makes A decide first whether
or not to tender, then B, then C
David McAdams
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Zwest Game #2 (C first)

Zwest makes C decide first whether
or not to tender, then B, then A
David McAdams
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Play Zwest Games!

Group into three pairs to play (you and a
partner will play together)
• Roll a die to see who is A, B, C

With your partner decide which game you
would rather be playing (in your role),
and write this down with your names and
a brief explanation
• Your choice will not affect which game you
ultimately play
David McAdams
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Play Zwest Games!

I’ll inform you which game your
group will be playing

Record the progress and the results
on the sheet given to you
David McAdams
19
Commitment
“The Power to Constrain an
Adversary Depends Upon the
Power to Bind Oneself.”
- Thomas Schelling
Commitment in the
Examples We’ve Seen

Campeau committed to paying the
high price $110 even if he failed to
gain control
• This allowed him to avoid failure, since
shareholders would all want to tender if he
were going to fail

Qwest committed not to renegotiate
later with the non-tenderers
David McAdams
21
Game within a Game

So far, we have examined hostile
takeovers as a voting game played
among the target’s stockholders

But actually the shareholder vote is a
“game within a game”
• Entrenched management, the raider, and other
suitors strategize over influencing shareholders’
options and incentives in the forthcoming vote 
That in itself is a game …
David McAdams
22
Bitter Pills

Numerous ways for entrenched
management to increase the cost of
a takeover (“Shark Repellant”)
• “Poison Pills”
• “Macaroni Defense”

… and for raiders to fight back
• “Lady MacBeth Strategy”
• “Saturday Night Special”
David McAdams
23
Saturday Night Specials
“From the hostile bidder’s perspective,
the most critical element – in contrast to
substantive matters such as the price
offered and the number of shares sought
– is speed … If the hostile bidder can
structure its offer so that target
shareholders must decide to tender
before a competitive bid can be arranged,
a substantial advantage will be secured”
- Source, Gibson and Black (1995), “The Law and Finance of
Corporate Acquisitions”
David McAdams
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Game within a Game within
a Game (within a Game)


Management needs shareholders to
approve a Poison Pill. Thus, shareholders
and management play a game long
before raider arrives.
Yet one layer deeper: Poison Pills remove
management’s incentive to take more
drastic, self-destructive behavior
• If management can commit to adopt such a
“Scorched-Earth Policy”, then shareholders will be
more willing to grant a Poison Pill
David McAdams
25
Role of Regulation


Players may strategically commit to
strategies that reduce overall gains from
the game.
Beneficial regulation shapes the options
available to players so that the options
they will likely choose lead to better
outcomes.
• Saturday Night Specials were made illegal by the
Williams Act of 1968, which stipulated that any
tender offer must be kept open for at least 20 days.
David McAdams
26
Bubbles
“We thought it was the 8th inning,
and it was the 9th”
- Stanley Druckenmiller, former manager of Soros’ Quantum
Fund, April 2000.
“Julian said, ‘This is irrational and I won’t play”,
and they carried him out feet first.
Druckenmiller said, ‘This is irrational and I’ll
play’, and they carried him out feet first.”
-
NYTimes April 29, 2000: “Another Technology Victim; Soros Fund Manager Says He
‘Overplayed’ Hand”. (Julian Roberts managed Tiger Hedge Fund, dissolved in 1999.)
Bubbles: Game Plan
1.
Newspapers, academics, and
crystal balls…
2.
Should you sell when you know
you are in a bubble?
3.
Bubble Game
4.
Lessons learned: Bubble Game
David McAdams
28
Newspapers, academics, and
crystal balls …

Spotting trends

The January Effect
David McAdams
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Spotting trends








“__
“__
“__
“__
is typically a strong month for stocks”
tends to be a good month for stocks”
has historically been a strong month”
is usually a great month for stocks”
“__
“__
“__
“__
is often a negative month for stocks.”
tends to be a bad month for stocks”
is traditionally a poor month for stocks”
is a scary month for stocks”
David McAdams
30
Spotting Trends
Mark Twain, in Pudd’nhead Wilson:
“October. This is one of the
peculiarly dangerous months to
speculate in stocks in…
“The others are July, January,
September, April, November, May,
March, June, December, August,
and February.”
Spotting trends
Sources: Motley Fool, CNN, USA Today, Dow Jones, Dean Inv. Ass.
Good:
 Bad:



Jan, June, July, Dec
Mar, Aug, Sep, Oct
If each month is equally likely to go up or down,
there is an 80% chance that some month will be
“bad” three years in a row!
80% of the time, a naïve analyst will identify
(with 95% false confidence!) a day of the month
on which the markets have historically
performed better than average.
David McAdams
32
January Effect

Tendency of the stock market to rise
between December 31 and the end of the
first week in January.

Well-documented by a spate of scholarly
research in the 1980s
David McAdams
33
Sampling of Research
(USA data up to 80s)

In equally-weighted portfolio, average
return 3.5% in January, only .5% in others
• Excess returns not seen in DJIA, so effect limited
to and more pronounced in small stocks
• Over half of excess return on small stocks in Jan.

Excess returns greatest for small firms
whose prices have declined previous year
• Excess returns in first five days not observed for
“winners” of previous year
David McAdams
34
Sampling of Research
(non-USA data up to 80s)

January returns exceptional in 15/16
countries studied.
• In Belgium, Netherlands, Italy, January return
exceeds the return for the whole year!

Taxes appear confirmed as part of story
• Britain has April effect, Australia has July effect.

January itself seems significant
• Effect in Japan (where no capital gains) as well as
Britain and Australia.
David McAdams
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What Should You Do?

Careful research has shown that
there was a January effect from
1900-1980.

Should you go buy small-caps this
December?
David McAdams
36
January Defect?
Source: The Independent Adviser for Vanguard Investors,
December 10, 2002

“In the past few years, the January
effect has been more of a January
defect as investors, trying to get an
edge on their competitors, have
jumped earlier and earlier. In some
cases the January effect takes place
in November or even December.”
David McAdams
37
Most Recent Research

The Declining January Effect:
Evidences from the U.S. Equity
Markets Source:Quarterly Review of
Economics and Finance v43, n2 (Summer
2003): 395-404
David McAdams
38
Bubbles

What is a bubble?

How do bubbles start?

How do bubbles persist?

How do bubbles burst?
David McAdams
39
A Simple Model of Bubbles

A structural change leads unsophisticated
investors to conclude there is a “new
economy” with permanently higher
growth (and permanently rising prices!).
• South Sea bubble in 1700s
• Tech bubble in 1990s

BUT sophisticated investors know that the
growth spurt is temporary and will return
to normal levels
• Still, no one knows how long high growth will last
This model is based on Abreu and Brunnermeier, “Bubbles and Crashes”,
Econometrica (2003)
David McAdams
40
A Simple Model of Bubbles


Sophisticated investors begin to realize
that the growth spurt has ended after the
fact and not all at the same time.
As long as a majority of sophisticated
investors stay invested, price continues to
increase at a high rate. (This is an assumption.)
• For our purposes, “bubble” = majority of
sophisticated investors know that growth has
stopped, but still a majority stays invested.

BUT once a majority of sophisticated
investors have sold, the naïve realize
their error and the bubble bursts.
David McAdams
41
How Do Bubbles Start?
You are an investor in the early
1700s.
 The masses believe that the South
Seas Company’s price is sure to rise
at high rates permanently.
 To your surprise, you learn that
South Seas trade is a dud!
Should you sell immediately?!

David McAdams
42
Bubble Game: Rules


5 players
10 periods. Decide Buy/Sell in each
• After period 10, Price will revert to Value

Price process
• Price = Value = $1 at start
• Price doubles each period until 3 or more
sophisticates have sold

Player payoffs
• Once you Sell, you are done and get current price.
• If you still own when 3 others have sold, you get
current Value
David McAdams
43
Bubble Game: Rules

Value process
• Value doubles each period during the growth period.
• I will flip a coin each period to determine whether
growth has ended (beginning after round 1).
• Example: If growth stops after round 3, then value =
price ($1, $2, $4) in periods 1,2,3 but value = $4 in
all periods T > 3 whereas price keeps on doubling.
When bubble bursts, price falls back to $4.

Information process
• Once growth ends, one randomly chosen player will
immediately learn that it has ended
• The next period, a second player will learn that it
has ended, and so on
• Note: Upon learning, you don’t know if you were the
first to learn, the second, … or the last!
David McAdams
44
Sell Immediately Upon
Learning: Nash Equilibrium?

Suppose that all others are following
the strategy of selling immediately
upon learning that growth has
stopped (but not before)

Should you sell immediately upon
learning yourself?
David McAdams
45
How Do Bubbles Persist and
Burst?


Play the Bubble Game to find out!!
Form groups of four or five so that there
are ten groups total
• Select one from among you to represent your group.
• Discuss among yourselves how to play – no discussion
will be allowed once game begins
• Consult hand-out for more detailed info on game

We will play two iterations of the Bubble
Game, then discuss for lessons learned
David McAdams
46
News and “Overreaction”




We have seen that bubbles can exist even
when there are numerous rational players
BUT bubble can only persist when these
players are relatively uncertain about
when others are going to sell
Even small news events can serve as
coordinating devices that allow / force the
rational investors all to escape the bubble
The response is not an “overreaction” to
the news but the bubble bursting
• Note: This does not explain why the stock market
moves a lot with every news story.
David McAdams
47