The fact that decisions can be altered by the expectation of their consequences has lots of implications. In Game Theory 101 we talked about bluffing. Working out when promises or threats should be taken seriously and when they are (in game-theory-speak) “cheap talk” is fundamental to solving complicated situations in business, in politics, and in our daily encounters. Sorting out when promises or threats are sincere and when they are just talk is the problem of determining whether commitments are credible.
LET’S PLAY GAMES
In predicting and engineering the future, part of getting things right is working out what stands in the way of this or that particular outcome. Even after pots of money are won at cards, or hands are shaken and contracts or treaties are signed, we can’t be sure of what will actually get implemented. We always have to ask about commitments. Deals and promises, however sincerely made, can unravel for lots of reasons. Economists have come up with a superbly descriptive label for a problem in enforcing contracts. They ask, is the contract “renegotiation- proof”?3 This question is at the heart of litigiousness in the United States.
I once worked on a lawsuit involving two power companies. One produced excess electricity and sold it to a different electric company in another state. As it happened, the price for electricity shot way up after the contract was signed. The contract called for delivery at an agreed-upon lower price. The power seller stopped delivering the promised electricity to the buyer, demanding more money for it. Naturally, the buyer objected, pointing out that the contract did not provide for changing the price just because market conditions changed. That was a risk that the buyer and seller agreed to take when they signed their contract. Still, the seller refused to deliver electricity. The seller was sued and defended itself vigorously so that legal costs racked up on both sides. All the while that bitter accusations flew back and forth, the seller kept offering to make a new deal with the plaintiff. The deal involved renegotiating their contract to make adjustments for extreme changes in market prices. The plaintiff resisted, always pointing—rightly—to the contract. But the plaintiff also really needed the electricity and couldn’t get it anywhere else for a better price than the seller, my client, was willing to take—and my client knew that. Eventually, the cost of not providing the necessary electricity to their own clients became so great that the plaintiff caved in and took the deal they were offered.
Here was nasty, avaricious human nature hard at work in just the way game theorists think about it. Yes, there was a contract, and its terms were clear enough, but the cost of fighting to enforce the contract became too great. However much the plaintiff declared its intent to fight the case in court, the defendant knew it was bluffing. The plaintiff’s need for electricity and the cost of battling the case out in court were greater than the cost of accepting a new deal. And so it was clear that the terms of the contract were not renegotiation-proof. The original deal was set aside and a new one was struck. The original deal really was not a firm commitment to sell (or probably, for that matter, to buy) electricity at a specified price over a specified time period when the market price moved markedly from the price stipulated in the agreement. Justice gave way, as it so often does in our judicial system, to the relative ability of plaintiffs and defendants to endure pain.
Commitment problems come in other varieties. The classic game theory illustration of a commitment problem is seen in the game called the prisoner’s dilemma, which is played out on almost every cop show on TV every night of the week. The story is that two criminals (I’ll call them Chris and Pat) are arrested. Each is held in a separate cell, with no communication between them. The police and the DA do not have enough evidence to convict them of the serious crime they allegedly committed. But they do have enough evidence to convict them of a lesser offense. If Chris and Pat cooperate with each other by remaining silent, they’ll be charged and convicted of the lesser crime. If they both confess, they’ll each receive a stiff sentence. However, if one confesses and the other does not, then the one who confesses—ratting out the other—will get off with time served, and the other will be put away for life without a chance for parole.
It is possible, maybe even likely, that Chris and Pat, our two crooks, made a deal beforehand, promising to remain silent if they are caught. The problem is that their promise to each other is not credible because it’s always in their interest—if the game is not going to be repeated an indefinite number of times—to renege, talking a blue streak to make a deal with the prosecutor. Here’s how it works:
THE PRISONER’S DILEMMA
Pat’s Choices >
Chris’s Choices
v
Don’t confess (stay faithful to Chris)
Confess (rat out Chris)
Don’t confess (stay faithful to Pat)
Chris and Pat get 5 years
Chris gets life; Pat gets time served
Confess (rat out Pat)
Chris gets time served; Pat gets life
Chris and Pat get 15 years
After Chris and Pat are arrested, neither knows whether the other will confess or really will stay silent as promised. What Chris knows is that if Pat is true to his word and doesn’t talk, Chris can get off with time served by betraying Pat. If instead Chris stays faithful to her promise and keeps silent too, she can expect to get five years. Remember, game theory reasoning takes a dim view of human nature. Each of the crooks looks out for numero uno. Chris cares about Chris; Pat looks out only for Pat. So if Pat is a good, loyal buddy—that is, a sucker—Chris can take advantage of the chance she’s been given to enter a plea. Chris would walk and Pat would go to prison for life.
Of course, Pat works out this logic too, so maybe instead of staying silent, Pat decides to talk. Even then, Chris is better off confessing than she would be by keeping her mouth shut. If Pat confesses and Chris stays silent, Pat gets off easy—that’s neither here nor there as far as Chris is concerned—and Chris goes away for a long time, which is everything to her. If Chris talks too, her sentence is lighter than if she stayed silent while Pat confessed. Sure, Chris (and Pat) gets fifteen years, but Chris is young, and fifteen years, with a chance for parole, certainly beats life in prison with no chance for parole. In fact, whatever Chris thinks Pat will do, Chris’s best bet is to confess.
This produces the dilemma. If both crooks kept quiet they would each get a fairly light sentence and be better off than if both confessed (five years each versus fifteen). The problem is that neither one benefits from taking a chance, knowing that it’s always in the other guy’s interest to talk. As a consequence, Chris’s and Pat’s promises to each other notwithstanding, they can’t really commit to remaining silent when the police interrogate them separately.
IT’S ALL ABOUT THE DOG THAT DIDN’T BARK
The prisoner’s dilemma illustrates an application of John Nash’s greatest contribution to game theory. He developed a way to solve games. All subsequent, widely used solutions to games are offshoots of what he did. Nash defined a game’s equilibrium as the planned choice of actions—the strategy—of each player, requiring that the plan of action is designed so that no player has any incentive to take an action not included in the strategy. For instance, people won’t cooperate or coordinate with each other unless it is in their individual interest. No one in the game- theory world willingly takes a personal hit just to help someone else out. That means we all need to think about what others would do if we changed our plan of action. We need to sort out the “what ifs” that confront us.
Historians spend most of their time thinking about what happened in the world. They want to explain events by looking at the chain of things that they can observe in the historical record. Game theorists think about what
