## LESSWRONGLW

Vanessa Kosoy's Shortform

Game theory is widely considered the correct description of rational behavior in multi-agent scenarios. However, real world agents have to learn, whereas game theory assumes perfect knowledge, which can be only achieved in the limit at best. Bridging this gap requires using multi-agent learning theory to justify game theory, a problem that is mostly open (but some results exist). In particular, we would like to prove that learning agents converge to game theoretic solutions such as Nash equilibria (putting superrationality aside: I think that superrational

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Instead of postulating access to a portion of the history or some kind of limited access to the opponent's source code, we can consider agents with full access to history / source code but finite memory. The problem is, an agent with fixed memory size usually cannot have regret going to zero, since it cannot store probabilities with arbitrary precision. However, it seems plausible that we can usually get learning with memory of size . This is because something like "counting pieces of evidence" should be sufficient. For example, if consider fini