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ECON-159: GAME THEORY
Lecture 22 - Repeated Games: Cheating, Punishment, and Outsourcing [November 28, 2007]
Chapter 1. Repeated Interaction: The Grim Trigger Strategy in the Prisoner's Dilemma (Continued) [00:00:00]
Professor Ben Polak: So last time we were focusing on repeated interaction and that's what we're going to continue with today. There's lots of things we could study under repeated interaction but the emphasis of this week is can we attain — can we achieve — cooperation in business or personal relationships without contracts, by use of the fact that these relationships go on over time? Our central intuition, where we started from last time, was perhaps the future of a relationship can provide incentives for good behavior today, can provide incentives for people not to cheat.
So specifically let's just think of an example. We'll go back to where we were last time. Specifically suppose I have a business relationship, an ongoing business relationship with Jake. And each period I'm supposed to supply Jake with some inputs for his business, let's say some fruit. And each period he's supposed to provide me with some input for my business, namely vegetables. Clearly there are opportunities here, in each period, for us to cheat. We could cheat both on the quality of the fruit that I provide or the quantity of the fruit that I provide to Jake, and he can cheat on the quantity or quality of the vegetables that he provides to me. Our central intuition is: perhaps what can give us good incentives is the idea that if Jake cooperates today, then I might cooperate tomorrow, I might not cheat tomorrow. Conversely, if he cheats and provides me with lousy vegetables today I'm going to provide him with lousy fruit tomorrow. Similarly for me, if I provide Jake with lousy fruit today he can provide me with lousy vegetables tomorrow.
So what do we need? We need the difference in the value of the promise of good behavior tomorrow and the threat of bad behavior tomorrow to outweigh the temptation to cheat today. I'm going to gain by providing him with the bad fruit or fewer fruit today — bad fruit because those I would otherwise have to throw away. So that temptation to cheat has to be outweighed by the promise of getting good vegetables in the future from Jake and vice versa. So here's that idea on the board. What we need is the gain if I cheat today to be outweighed by the difference between the value of my relationship with Jake after cooperating and the value of my relationship with Jake after cheating tomorrow.
Now what we discovered last time — this was an idea I think we kind of knew, we have kind of known it since the first week — but we discovered last time, somewhat surprisingly, that life is not quite so simple. In particular, what we discovered was we need these to be credible, so there's a problem here of credibility. So in particular, if we think of the value of the relationship after cooperating tomorrow as being a promise, and the value of the relationship after cheating as being a threat, we need these promises and threats to be credible. We need to actually believe that they're going to happen.
And one very simple area where we saw that ran immediately into problems was if this repeated relationship, although repeated, had a known end. Why did known ends cause problems for us?