A Prisoner of Your Own Dilemma

Imagine you are in 1988. You’ve just combed your mullet, threw on your Italian blazer over your pink T-shirt and slipped on your sockless loafers when the phone rings. It’s your stock broker. He needs to talk to you urgently about two offers that have come in for your shares in Federated Department Stores.

"Offers?", you wonder, "I didn’t realize Federated was doing so well. Did I miss something?"

It seems you’ve forgotten that you’re in 1988 in the heyday of corporate raiders and junk bond leveraged buyouts. Federated wasn’t actually doing great but was surviving fine. Shares were fairly valued about $100 and were stable enough that they’d stay around the same price even after the dust settled from a takeover.

Your broker tells you that Macy’s is making a move to take over Federated.

"They’re offering $102 per share, $2 more than they are worth now."

"Take it," you tell him.

"Hold on," he says. "The offer is conditional on them getting 50% of share offers. If they don’t get at least 50%, they don’t buy the shares and they’re back at $100.

You do the math. “Let me get this straight,” you tell him, “My options are to either turn it down and keep my $100 shares or, if I accept the offer, the best case is I get $102 and the worst case is I get my $100 shares back?”

"Yes," he says, "That’s correct."

"Well then, there’s nothing to lose by accepting the offer, right?"

"Hold on; not so fast," your broker cautions, "I told you there were two offers. There’s another takeover bid from some guy named Robert Campeau.”

Robert Campeau was a successful real estate developer of the 1960s and 70s in Ottawa, Ontario, famous for his controversial housing developments, particularly in the Ottawa suburb of Kanata where a street he help develop now bears his name. During the height of the cold war, Ottawa mayor Charlotte Whitton famously quipped, “When I look at his houses, I think perhaps nuclear bombardment might not be such a terrible thing after all.”

In the 1980s, Robert Campeau turned his business interests towards a series leveraged buyouts, including Federated Departments Stores, hence his offer to buy your shares. This offer was different from Macy’s though. It was a two-tier offer. He was offering $106 per share, unconditional on him getting 50%. But he’d only offer $106 for the first 50% of all outstanding shares. For every additional share after that, he’d offer $90.

"We’d better take that offer fast," you tell your broker.

"No, no. It doesn’t work that way," he replies.

He explains to you that it’s not first come, first serve. Rather, it operates like a fund. For every offer of shares that Campeau receives he’ll put $106 in the fund. Once he gets over 50% of all shares offered to him, he’ll put $90 into the fund for each new one. When the deadline passes, the total fund will be divided amongst all the offered shares. You’d get a blended amount of the two depending on what percentage of shares were offered to him. If 50% or less shares are offered to him, you’d get $106 per share. If 100% of shares are offered, you’d get $98 — the average of $106 and $90. For percentages between 50% and 100%, the blended amount scales from $106 to $98. At 66.7% you’d get $102 per share, the same as Macy’s offer. At 80% you’d get $100. So only above 80% would you actually lose money.

"That sounds riskier," you say. "I might lose money where I’m guaranteed not to lose anything on the Macy’s offer."

"There’s a catch," your broker explains. "If Campeau gets more than 50% of the shares offered, he gets control of the company and he will take it private. That means he can forceably take your share for his lowest price offered per share, which is $90.

"That’s even scarier," you claim. "That should scare off everyone from offering to him to make sure he doesn’t get control."

"No," says your broker, "You haven’t thought this through. If you think he’ll get less that 50% of the shares, you are better off offering to him because you’ll get $106 per share. If you think he’ll get more than 50% of the shares you are also better off offering to him because if you don’t, he’ll just take them for $90. At least if you offer to him the lowest you can make is $98. Either way, you are better off offering them to Campeau regardless of what anybody else does."

You are impressed with your broker. “Wow, did you figure that all out by yourself? You are pretty smart when it comes to trading shares.”

"Well," he replies, "I’d like to take credit for figuring that out, but Campeau spelled it all out in great detail to all of the shareholders so that everyone could clearly see they were better to offer to him."

Although your image of your broker’s prowess is now slightly deflated, you agree it is the best option to offer your shares to Campeau and give him instructions to do so.

The deadline passes and the offers go through. Your broker calls you again. You turn the volume down on your new Compact Disc player belting out Def Leppard.

"How did we do?" you ask frantically.

"Well," he says hesitantly, "you sold all of your shares to Robert Campeau for $98."

"What?" you exclaim. "You mean everybody offered them to Campeau?”

Your broker pauses for a moment. “Yes, of course. Remember that offering to Campeau was in your best interest no matter what anybody else did, right? Well, the same was true for everybody else too. So they all offered.”

"Wait. You mean to tell me that we all had the opportunity to make $2 per share by offering to Macy’s and yet we all sold to Campeau at a $2 loss because it was in our best interest in a free market? I think perhaps nuclear bombardment might not be such a terrible thing after all."

The Dilemma

So what did you do wrong? How is it that you lost $2 when you could have earned $2 by offering to Macy’s. The answer is, sadly: nothing.

It’s even more depressing than that. Imagine if you get a do-over. Suppose Campeau was a really nice guy and offered to let any of the shareholders change their minds. Would you switch to Macy’s now, or hold onto it?

Just remember, if you think everybody else will switch to Macy’s for $102 then you are better off sticking with Campeau for $106. It doesn’t even need to be everybody else. If you think even 50% or more of people will switch to Macy’s you can still get $106 from Campeau. Or, if you think even 34% of people will switch to Macy’s you’ll still get slightly more from Campeau ($102.12).

If, on the other hand, you thought that less than 50% of people would switch then you’d still be better sticking with Campeau, otherwise he’ll take your shares for $90.

Even with a do-over, you should still stick with Campeau, as should everybody else, and so you’ll still all lose $2 when you have an opportunity to gain $2. Why is this?

The scenario here describes one of the more famous examples of what’s called a Prisoner’s Dilemma. (The name comes from its original description in game theory having to do with prisoners ratting each other out, but I find this monetary one more illustrative and also based on the very real story of Campeau’s takeover of Federated, though simplified here for illustrative purposes.)

The generalized Prisoner’s Dilemma can be summarized by the following rules given two options, A and B:

  • If most people chose A, you get a small reward (or none) by also choosing A but a big reward by choosing B.
  • If most people chose B, you get a big penalty by choosing A but a small penalty by choosing B.

Faced with these options you are always best with B, and so is everybody else, so you all pay a small penalty even though A offers a reward.

If you are smart, and slimy, you might be able to convince everybody else to chose A while you chose B. Then you are benefiting from their sacrifice so that you can make more at their expense. That might work if most people aren’t smart enough to notice or understand the situation.

The Prisoner’s Dilemma models many collective transactions. Consider laws. Suppose there were no laws against theft. If most people chose not to rob each other, you get the benefit of that safety. You are very unlikely to get robbed because most other people chose not to do that. But you’d get a better payoff if you decided to rob other people. Then you get both the benefit of other people not robbing you, but you get to rob them and they can’t do anything about it. Consequently, it only takes one bad apple to spoil the party. When others see you robbing and benefiting from their sacrifice (and their stuff), they will tend to be worse off it they too don’t starting robbing other people. So, everyone starts robbing each other and now you lose that benefit and pay the penalty of having your stuff taken. (This is essentially what happened in the very real circumstances of competing air squadrons I described in an earlier post.)

Sure, this isn’t the pure motivator of people. (Evolutionary psychology would actually say it likely is as this scenario would drive the evolution of instinctive social rules, but that’s a separate issue for now.) The point here is that pure individualism, with individuals seeking their own best interests, cannot solve this problem.

But there is a solution. Let’s go back to Campeau for another do-over. Suppose all of the Federated shareholders got together and made a binding pact: we will all offer to Macy’s instead. What do I mean by “binding”? It can’t just be a gentleman’s agreement. Then you benefit by breaking the agreement. There needs to be some enforceable penalty. So, we shareholders create an agreement in which we will be penalized if we offer to Campeau. Perhaps the penalty will be to have our legs broken, though a simple $5 fine per share would be enough to make Macy’s a better offer. The problem is we need the agreement to be enforceable. So we create an enforcement committee with authority to penalize ourselves if we break the rule, and vote some people onto the committee to enforce it. As long as we have enough people that will back the enforcement, we can even force the hand of those who don’t agree with this solution. We tell them it’s too bad they don’t agree, but we’ll break their legs (or take $5 per share from them by force) if the offer to Campeau.

Then it is in everyone’s best interest to offer to Macy’s and we can be confident that if anybody offers to Campeau they will be punished and be worse off than we are. So we all offer to Macy’s for $102 and make $2 per share.

Let me re-cap in slightly different terms. The solution that is our best individual interest is remove our right to individually chose. We can only get our best individual result by forcing everyone to follow a mandatory rule of collective best interest. In order for it to be enforceable, we need to create an organization that works on our own behalf to bind us to our common agreement.

To be clear, we don’t voluntarily choose to join a collective best interest. We aren’t getting some collective efficiency out of it like a group buying products in bulk for its members. We are forcing a mandatory choice on everyone, and it has to be on everyone, otherwise those who opt out benefit from everybody else’s sacrifice, so everybody opts out and we lose the benefit. We also are not voluntarily sacrificing an individual loss to be altruistic for some common good. We are maximizing our own individual payoff. Without the mandatory rule, we lose $2. With it, we gain $2.

Has it sunk in yet? What I am talking here is the very basis for democratic government. As a bunch of individuals seeking our own best interests, we can get by. But in a world of “everybody for themselves” it is might that makes right. If you try to get ahead, somebody can just take your stuff. You need to expend some of your resources defending it. That effort is a penalty to you, even if you manage to successfully defend your stuff.

It is when we bind ourselves to the collective best interests that we do better even as individuals. It is when we create an organization that works for us, on our behalf, to enforce our common rules even on ourselves, that we prosper the most. Any transaction where we get better payoffs by binding ourselves to a mandatory option can be modeled as a Prisoner’s Dilemma.

It’s how we get roads built. It’s where we get police, and fire, and health care. It’s what justifies the mandatory taxes for them. It’s where laws come from, and their enforcement. It might even justify things like a mandatory census if the value that census produces exceeds the risk of having to fill one out. If enough people (in sufficient demographic distribution) volunteer to fill it out then you are better off not filling it out; you save the effort and “intrusion”. If not enough people volunteer to fill it out to make it have value to you, you are better off not filling it out as well. So few fill it out, it becomes worthless, and you don’t gain the net value from the census anymore. Congratulations, you’ve chosen the $98 option over the $102 option.

That doesn’t mean everything government does is justified. Of course not. But it does indicate what things the government is justified in doing on our behalf, even when some people object. It also explains why societies with government do better than those without, and why those with democratic government do better than those with private governments. (By private government I mean those who govern for personal, private benefit such as monarchies, dictators, despots, and warlords.)

You will always get those who object. Libertarians will say that people should have the option. Ayn Rand Objectivists will say that individuals are best to select their own best interest. Neo-conservatives will say mandatory collective rules is socialism (and mean it in a bad way). They will all say that the government is interfering in their choice and that they could earn $106 if only the government would get out of the way and remove the rule forcing them to chose Macy’s $102.

But they are all short-sighted. The $106 is an illusion. It’s there on paper only. In reality, if you get rid of the rule, you will only get $98. Or, you will get the manipulative experts convincing everyone else to select the Macy’s offer while they offer to Campeau, and benefit off the sacrifice of others via ignorance.

Keep that in mind when judging political rhetoric on the “right” size of government. Smaller isn’t always better.