Strategic Economics

Repeated Games and the Folk Theorem

Work out exactly how patient two parties have to be for a handshake to hold, and why the same arithmetic that makes a supplier relationship work is what competition authorities are looking for between rivals.

  • Expert
  • 15 min total
  • 14 chapters

What decision this helps you make: Whether an unenforceable arrangement will actually be honoured, and which of the three levers (horizon, observability, and the cost of retaliation) you can move to make it hold.

What this topic is

A repeated game is the same strategic situation played over and over by the same parties. The folk theorem is the central result about them: if the players are patient enough, care enough about the future, and can see what each other did, then almost any outcome that leaves everyone at least as well off as they could guarantee themselves alone can be sustained as an equilibrium. That includes cooperative outcomes which are strictly impossible in a single encounter, and it includes a great many bad ones too.

Why it matters

Most commercial relationships are governed by far less contract than the value at stake would justify, and they work anyway. The reason is not goodwill; it is that both sides expect to be here next year and have run the arithmetic. That arithmetic is precise, it has three inputs, and every one of them is something you can change: how long the relationship is expected to last, how quickly a breach would be noticed, and how much the injured party could take away afterwards. When an informal arrangement stops working, one of those three moved.

Who should learn it

Anyone relying on a relationship that a contract cannot fully specify (supplier quality, channel discipline, referral reciprocity, employment), and anyone in a concentrated market who needs to understand where independent parallel conduct ends and unlawful coordination begins.

What you will understand

  • How to compute the critical discount factor at which an informal arrangement becomes self-enforcing, from your own numbers
  • Why a four-period detection lag can raise that threshold from 0.50 to about 0.84, and what that means operationally
  • Why the folk theorem proves too much to be a prediction, and what it is genuinely good for instead
  • The precise boundary between a lawful long-term relationship and unlawful coordination between competitors

Prerequisites

Common misconception

"Repeated interaction makes people cooperate." It makes cooperation possible, which is a different and weaker claim. The folk theorem says that with enough patience the set of sustainable outcomes expands to include almost everything between the worst each party can be held to and the best jointly available: the cooperative outcome, the non-cooperative one, and a continuum of asymmetric arrangements in which one side does most of the giving. Nothing in the result selects among them. A long relationship is not evidence that the terms are fair; it is evidence only that both sides prefer them to a fight.