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This is: In Logical Time, All Games are Iterated Games, published by Abram Demski on the AI Alignment Forum.
Logical Time
The main purpose of this post is to introduce the concept of logical time. The idea was mentioned in Scott's post, Bayesian Probability is for things that are Space-like Separated from You. It was first coined in a conference call with, Daniel Demski, Alex Mennan, and perhaps Corey Staten and Evan Lloyd -- I don't remember exactly who was there, or who first used the term. Logical time is an informal concept which serves as an intuition pump for thinking about logical causality and phenomena in logical decision theory; don't take it too seriously. In particular, I am not interested in anybody trying to formally define logical time (aside from formal approaches to logical causality). Still, it seems like useful language for communicating decision-theory intuitions.
Suppose you are playing chess, and you consider moving your bishop. You play out a hypothetical game which results in your loss in several moves. You decide not to move your bishop as a result of this. The hypothetical game resulting in your loss still exists within logic. You are logically later than it, in that the game you actually play depends on what happened in this hypothetical game.
Suppose you're stuck in the desert in a Parfit's Hitchhiker problem. Paul Ekman is reading your face, deciding whether you're trustworthy. Paul Ekman does this based on experience, meaning that the computation which is you has a strong similarity with other computations. This similarity can be used to predict you fairly reliably, based on your facial expressions. What creates this similarity? According to the logical time picture, there is a logical fact much earlier in logical time, which governs the connection between facial expressions and behavior.
To the extent that agents are trying to predict the future, they can be thought of as trying to place themselves later in logical time than the events which they're trying to predict. Two agents trying to predict each other are competing to see who can be later in logical time. This is not necessarily wise; in games like chicken, there is a sense in which you want to be earlier in logical time.
Traditional game theory, especially Nash equilibria, relies on what amounts to loopy logical causality to allow each agent to be after the other in logical time. Whether this is bad depends on your view on logical time travel. Perhaps there is a sense in which logical time can be loopy, due to prediction (which is like logical time travel). Perhaps logical time can't be loopy, and this is a flaw in the models used by traditional game theory.
Iterated Games
In logical time, all games are iterated games. An agent tries to forecast what happens in the decision problem it finds itself in by comparing it to similar decision problems which are small enough for it to look at. This puts it later in logical time than the small examples. "Similar games" includes the exact same game, but in which both players have had less time to think.
This means it is appropriate to use iterated strategies. Agents who are aware of logical time can play tit-for-tat in single-shot Prisoner's Dilemma, and so, can cooperate with each other.
Iterated games are different in character than single-shot games. The folk theorem shows that almost any outcome is possible in iterated play (in a certain sense). This makes it difficult to avoid very bad outcomes, such as nearly always defecting in the prisoner's dilemma, despite the availability of much better equilibria such as tit-for-tat. Intuitively, this is because (as Yoav Shoham et al point out in If multi-agent learning is the answer, what is the question?) it is difficult to separate "teaching behavior" from "learning behavior": as in the tit-for-tat s...
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