Bargaining into Anarchic Order

A long time ago, my friend and colleague Gordon Tullock wrote a chapter for a book on anarchy in which he argued that it was impossible to bargain one’s way out of Hobbesian anarchy, the war of each against all. His argument was simple: Until you had a state, no contract, including that one, could be enforced, so making a contract had no effect. Reading it, I concluded that the argument was both obvious and wrong. As anyone who knew Gordon would understand, the opportunity to say so, if possible in print, was one I could not resist, so I wrote a review of the book. This chapter is based on the argument of that review.

Arnold and Bill are the only inhabitants of a small Hobbesian anarchy: no government, no customs, no pre-existing rules. It occurs to both of them that the situation has serious problems. Anything one of them gathers, the other might steal, and spending full time guarding things makes it hard to gather more. A possible solution is for one of them to kill the other; adequate precautions to prevent that will make it hard to do much else. There should be a better way.

Arnold proposes one. There is a stream running though the forest. He will take one side of it for his territory, Bill the other side for his. Each will agree not to trespass on the other’s territory without permission. The agreement will be enforced by the threat of violence; Arnold makes it clear that if he finds Bill on his side of the stream after they have agreed to the division, he will do his best to beat him up, and that he expects Bill to behave similarly. A fight to the death is likely to be a losing proposition even for the winner, so each has a clear incentive to abide by their agreement, provided that each believes the other is committed to enforcing it.

Arnold and Bill have just created private property in land. They have done so by reinventing territorial behavior, a survival strategy practiced by various species of animals, mostly birds and fishes. Territorial animals mark the territory they claim and enforce the claim to territory by a commitment strategy, by somehow turning a switch in their brain that makes them attack a trespasser of their own species more and more fiercely the further into the territory he comes. Unless the trespasser is much larger than the defender, a fight to the death is a loss for both, so once the trespasser realizes the defender is commited to fight, he retreats..

Time passes. Arnold locates, a grove of apple trees, clears out the surrounding undergrowth and harvests the fruit. Bill has found an outcropping flint, chipped himself an axe, and is using it to cut down some trees in order to build a hut—he is tired of being rained on. One day Bill notices Arnold, on his side of the creek, watching him work, and comes over to chat—politely leaving his axe behind.

Arnold has a deal to propose. If Bill will cut down several large trees currently shading the apple grove, Arnold will promise to give Bill a bushel of apples from each year’s harvest. Bill agrees to the deal and performs his part of the contract.

Arnold considers the possibility of reneging on his—picking a bushel of apples is a fair amount of work and, once picked, he would rather eat them himself than hand them over to Bill. It occurs to him, however, that Bill still has an axe and can use it, if he wants, against Arnold’s apple trees the next time Arnold is somewhere else. Or, if he prefers, against Arnold. He decides to deliver the apples as per contract.

The reason Bill gets the apples is not that he has cut down shade trees but that he can cut down apple trees—once the contract is agreed to, it is the threat, not the past performance, that makes Arnold deliver. Why couldn’t Bill have saved himself a considerable amount of work by starting with the threat, telling Arnold that he will cut down the apple trees unless Arnold pays him a bushel of apples not to? How, if at all, does making the initial agreement and performing Bill’s half of it change the strategic situation?

The answer requires a brief digression.

Schelling Points: The Idea

A professor calls a student into his Yale office and asks him to participate in an experiment with the possibility of a reward. The objective is to rendezvous with another student in New York city by both being at the same place at the same time. If they succeed, they will each get a hundred dollars. Neither knows the other’s name and, even if they know or guess it, they are not permitted to communicate before meeting.

To win the prize, each has to guess where and when the other will try to meet him. One way of doing so is to figure out what time and place each will see as unique, since if their criterion for choice yields more than one answer they might choose different answers and so miss each other. Time is pretty easy—given our system of time keeping, noon and midnight are the only times that appear unique. Which they choose will depend on how long it takes them to get from New Haven to New York and what hours they normally keep. If it does not take too long and they are not night owls, noon is the obvious choice.

Where is harder. When I first read about the problem, my suggestion was the top of the Empire State building. That was, at the time, the tallest building in the world, making it unique in a fairly obvious sense. It turned out, however, that there was no such place. The building had four observation decks spaced around the four sides, with no obvious way of deciding which one to meet at. I am told that in the real world experiment, proposed by Thomas Schelling some fifty years ago and later implemented by someone else, the students met under the clock at Grand Central Station, to them the obvious unique meeting place. At noon.

This is a story about coordination without communication. What makes it relevant to this chapter—and much else—is that that describes not only situations where you are unable to speak to each other but also situations where you can speak but neither party has a good reason to believe what the other says.

For that version of Schelling’s idea, replace our two Yale students with two bank robbers. Having pulled off a successful heist they must decide how to split the loot before going their separate ways—and if they argue about it for too long the police may show up. Each played a different role in the robbery and each believes that his contribution was larger than that of his accomplice. I predict that they will split the money evenly, not because either thinks that fair but because that is the one division that both see as unique, hence as an alternative to interminable bargaining. They can talk to each other, but if one insists that he will not agree to any division that gives him less than 60% of the money the other has no reason to believe him. Fifty-fifty is different.

The analysis applies to a wide variety of bargaining situations. Both parties are better off reaching agreement, each would prefer to do it on terms more favorable to himself, and the longer they bargain the less the benefit to be shared between them. In the case of the bank robbers, that is represented by the risk that the cops will show up. In union/management bargaining, lost wages and revenue during a strike. In bargaining over a treaty to end a war, lives lost and property destroyed. The logic of all three situations is the same.

Schelling Points: The Application

The deal by which Arnold and Bill established their mutual property rights was a result of the Schelling point provided by the stream that they chose as their boundary. Bill could have tried to insist on getting everything on his side of the stream plus a strip on the other side. Arnold could have made a similar demand. They could have tried to divide the territory on some other basis, drawing an arbitrary line determining what each got. Any of those alternatives would have raised the same problem faced by the bank robbers haggling over their loot. For any offer Bill can make, Arnold can make a counter offer more favorable to himself. If they bargain too long, they may starve—or one of them may lose patience and take a convenient opportunity to brain the other. The stream provides a division that is simple, unique, already defined.

Before the Apple contract was made, Bill could have tried to extort apples from Arnold. Doing so would have created a bargaining situation, a mutual threat game. They have a common interest in Bill refraining from using his axe on either Arnold or Arnold’s orchard. They have a conflict of interest over how many apples Arnold pays Bill. The one Schelling point in that strategic situation is for Bill to respect the original division of the land, leaving Arnold with all his apples.

Once Bill has performed his half of the contract, there is a new Schelling point—for Arnold to pay Bill a bushel a year, as agreed. The agreement has changed the situation, not because either party considers himself morally bound to keep his word but because the agreement changes a fact that affects the outcome of their bargaining—the structure of the alternatives as both perceive it.

A different way of looking at the situation is to say that both Bill and Arnold have an incentive to establish a reputation for keeping their contracts, since that will permit further cooperation in the future—the discipline of constant dealings discussed back in Chapter 29 when I was explaining why firms would abide by their arbitration agreements. But we now have the tool to look into the question a little further.

Suppose Arnold renegs on his contract, pays no apples, and somehow gets away with it. Next year Arnold again wants Bill’s help. Bill’s response is proverbial: “Fooled me once, shame on you, fooled me twice, shame on me.” Arnold explains that he is wrong. It is true that Arnold broke his word once, but that was last year. Arnold explains that his policy, his consistent policy, is to break his word the first time, keep it forever after.

Why does Bill refuse to believe him? Because always keeping your word is a unique policy, a Schelling point. Keeping your word from the second year on is no more unique than keeping it on every other year, or every third year, or days when it doesn’t rain. No more unique than breaking it the first two years and then keeping it—and this is the second year. Schelling points help us understand why the discipline of constant dealings works: People perceive “always keep your word” as a unique policy, hence a Schelling point on which bargainers can converge.

I believe I have now shown why Gordon Tullock’s claim that, absent a government to enforce contracts, making a contract has no effect, hence individuals cannot bargain their way out of a Hobbesian anarchy. Making the contract changes the strategic situation by changing the pattern of Schelling points. Hence contracts are, to at least some degree, self-enforcing.