Case Study About Game Theory Youtube

In 1988, Canadian financier Robert Campeau was attempting a takeover of Federated, a retail congomerate that owned Bloomingdales.

The negotiations were quite interesting, and in 1990 Fortune magazine went so far as to call it “The Biggest, Looniest Deal Ever.”

One of the notable strategic elements was a “two-tiered offer” that Campeau made to shareholders. It was a good strategy but it did not work out exactly as planned.

Below we analyze this strategy in a simplified setting to see how it works.

Two-tiered offer: an intriguing strategy

The problem I describe is adapted from a case study in Thinking Strategically by Avinash Dixit and Barry Nalebuff.

The setting is as follows. Suppose you are one of three equal shareholders in a company. You have stock worth $100 per share and are considering two offers.

Option 1: Macy’s conditional offer
Macy’s makes an offer that is conditional on how many people offer to sell. If two or more people offer to sell–enough to guarantee a takeover–then Macy’s will pay $102 per share.

If only one person offers shares and a majority is not reached, then Macy’s will not buy any shares.

Option 2: Campeau two-tiered offer
Campeau makes a competing offer that is a bit more complicated.

He makes a two-tiered offer as follows. Campeau offers to pay a price that depends on the fraction of shares tendered.

Campeau will pay $105 for the first two people to offer shares (this is the first tier), and he will pay $87 for any remaining shares tendered (the second tier).

To be fair, the shares are not classified by order. Instead, if all three choose to tender, Campeau will pay a blended price to every person based on paying $105 for 2/3 of the shares and $87 for 1/3. Thus, each of the three shareholders get:

P = 105 (2/3) + 87 (1/3) = 99

To summarize, the options are as follows:

Macy’s offer: nothing if only one person offers, $102 if two or more people offer shares
Campeau pays out: $105 if one or two people offer shares, and $99 if all three offer

The question is: if every person chooses independently, which offer will win out?

Macy’s vs Campeau: who to pick?

What should be your decision if you are a shareholder? Do you tender or not?

It would seem the Macy’s offer is better because Campeau is offering a below market price if all three approve the deal.

But rather surprisingly, it is actually a dominant strategy to pick Campeau’s two-tiered offer!

To verify this, we can write out the strategies of each person and see what the best option is. You and the two other shareholders have the options of not tendering (N), tendering to Macy’s (M), or tendering to Campeau (C).

The two other shareholders can pick any of these 9 options. Just go through them and you can see that it is always a best response to offer to Campeau regardless of what the others do.

NN – the other two do nothing. If you play C you get $105 > $100 for M or C

NM or MN – one person offers to M. If you play C you get $105 > $102 for M

NC or CN – one person offers to C. If you play C you get $105 > $100

MM – two people offer to M. If you play C you get $105 > $102

MC or MC – your vote decides M or C. If you play C you get $105 > $102

CC – the others vote in C, so you would tender to C and get $99

So it is always in your best interest to tender shares to the two-tier plan of Campeau. By symmetry, this means everyone feels is is best to tender to Campeau.

Thus everyone ends up offering shares to to Campeau, and everyone ends up getting $99 in the two-tiered option. The individual choices prove to be short-sighted: had everyone cooperated to pick Macy’s, everyone could have gotten $102 instead.

The two-tiered option comes off as a kind of coercive strategy: shareholders have an incentive to offer shares early, but if everyone does this, then they all get paid out less.

How Macy’s could change the game

The two-tiered option is powerful but not necessarily unstoppable. The problem with Macy’s offer was the buying was conditional on getting a majority. Macy’s could instead make an unconditional offer of $102 per share.

Now the reasoning is slightly different. People will only tender to Campeau if they think exactly one or two people will tender to him, giving each a payout of $105.

If they expect everyone will tender to Campeau, then they would expect to get the blended price of $99 which is less than Macy’s offer of $102. There might still be trouble getting people to coordinate–the first few shares tendered are losing out on $105 in Campeau’s offer–but an unconditional offer gives Macy’s a small fighting chance.

An unfortunate ending for Campeau: how the strategy backfired

While Campeau used a good strategy in making his offer, things did not end up so well for him. As explained in these lecture notes

The actual unfolding of events were quite unfortunate for Campeau. Macy’s joined the bidding and this increased the premium quite signifcantly. Campeau finally won out (not by a two-tiered tender offer, however) but paid $8.17 billion for the stock of a company with a pre-acquisition market value of $2.93 billion. Campeau financed 97 percent of the purchase price with debt. Less than two years later, Federated fled for bankruptcy and Campeau lost his job

The debacle lives in infamy, and it was later even written that “Robert Campeau is considered by many as the best example of a fool,” according to Dale Arthur Oesterle in an issue of the Cato Review of Business and Government.

Game theory can help you achieve your outcome, but it can backfire if your goal was not worth pursuing.

More resources:

The biggest, looniest deal ever: Fortune Magazine 1990 article

Textbook explanation of Campeau’s acquisition of Federal: McGraw Hill

Cato Institute article about 80s mergers

- Он сказал, что на кольце были выгравированы какие-то буквы. - Буквы. - Да, если верить ему - не английские.

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