Rumours by Fleetwood Mac is, in my opinion, one of the best rock albums ever released. The sales charts bear out this appraisal, Rumours, like Dark Side of the Moon, set records that may never be broken (especially with the advent of digital music) for album sales. But what has this got to do with game theory?
One song on Rumours, which became Bill Clinton's campaign theme song many years after, is Don't Stop Thinkin' About Tomorrow. The song offers the upbeat message that the future always holds something better than the past and so one ought to concentrate on its possibility rather than dwelling in the shortcomings of the day before. Perhaps useful advice for a heart broken teenager but hardly the stuff of deep insight. (Indeed, almost bitter advice for someone like me, whose joints and musculature are progressively being turned to Swiss cheese by an autoimmune illness.) But anyway, back to our story.
The broader point of this song is that the actions of the present ought properly to be considered in light of the future. In other words, moving back one step, one choosing how to act, one ought properly never to stop "thinkin' about tomorrow" since it is the consequences of tomorrow that determine the costs and benefits of today's actions.
And, indeed, no better or deeper point can be made about the most important insight in all of game theory that, by harnessing the future, the present may be tamed.
Rewind to our one-off prisoners dilemma situation. This situation seems utterly hopeless and, in the vacuum outside time, is hopeless. It makes not difference the timing of moves nor the sophistication of opponents, the inexorable conclusion in such situations is that both parties are doomed to defect and thereby receive the lower rather than thre higher payoff. But if we place this situation back in
time, where there is a future, then a more palatable (and sensible) conclusion obtains. So long as both
parties don't stop Thinkin' about tomorrow, and so long as tomorrow is important enough, cooperation is possible. Indeed, this simple insight is at the heart of the vast majority of "contracting" occurring in the world.
While the word contract brings to mind the formality of legal documents, its underlying idea is not so formal. A contract is any agreement willingly undertaken by two parties. While we may think of such informal contracts as arm's length "handshake agreements" they need not be. Spouses deciding on a rotation of chores or child care is no less a contract for its informality. Roughly speaking, anything that trades off a present benefit for one in either another form (money, cooking, etc.) or time (tomorrow, a year from now) is a contract.
What game theory says is that, even if such contracts hold no water in any court of law, they still might be fulfilled so long as they are "self-enforcing" which is a fancy way of saying that both sides find it in their interests to execute on the contract rather than renege. Much of game theory is casting
about for circumstances in which contracts
The key, in many instances, is that both sides don't stop thinkin' about tomorrow, which disciplines their behavior today. While defecting on a relational contract might be a fine idea today, when it is your turn to give up value/spend cost, such behavior seems less good in light of what is given up over many tomorrows where no one is willing to engage in future relational contracts.
Curiously, social psychologists independently discovered this idea, albeit without the help of game theory. They talk of "equity theory", the idea that we each keep a mental account of favors granted and favors received for each acquaintance. According to this theory, when the accounts fall too far out of balance, relationships are "liquidated" ---in effect declaring bankruptcy on the friendship.
The point though is really the same. If it is better not to honor a relational contract than to do so, such agreements cease to be self-enforcing and breach becomes inevitable. Where psychologists would
differ concerns favors never asked for in the first place. For instance, Ann is sick and so Bob makes her pots and pots of chicken soup, which Ann abhors and has never requested. To an economist, Bob's offering Places Ann under no particular obligation to repay whereas a psychologist (and certainly my grandmother) would see this as an odious debt accrued by Bob from Ann's care and attention. Under the psych theory, Ann and Bob's relationship will likely founder over the unrequited chicken soup whereas an economist might see this as tangential, and indeed, irrelevant, to Ann and Bob's other dealings with one another.
Who do you think is corrcf? Our generic economist or my grandmother?