by Jessica Taylor 707 days ago | Stuart Armstrong likes this | link | parent You might be interested in a way of ensuring that 2 players always have the same mixed strategy in all Nash equilibria of some game: Assume we have a player $$A$$ and a player $$B$$. Player $$A$$ has some already-specified utility function; we would like player $$B$$ to play the same mixed strategy as $$A$$. Introduce a new player $$C$$ who gets to observe either $$A$$ or $$B$$’s action (unknown with 50% probability for each), and tries to determine who took this action (getting a utility of 1 for guessing correctly and 0 otherwise). $$B$$’s utility function is 1 if $$C$$ guesses incorrectly, and 0 if $$C$$ guesses correctly. $$B$$ will use the same mixed strategy as $$A$$ in all Nash equilibria. A similar method is used in the appendix A of the reflective oracles paper.

### NEW DISCUSSION POSTS

If you drop the
 by Alex Appel on Distributed Cooperation | 1 like

Cool! I'm happy to see this
 by Abram Demski on Distributed Cooperation | 0 likes

Caveat: The version of EDT
 by 258 on In memoryless Cartesian environments, every UDT po... | 2 likes

[Delegative Reinforcement
 by Vadim Kosoy on Stable Pointers to Value II: Environmental Goals | 1 like

Intermediate update: The
 by Alex Appel on Further Progress on a Bayesian Version of Logical ... | 0 likes

Since Briggs [1] shows that
 by 258 on In memoryless Cartesian environments, every UDT po... | 2 likes

This doesn't quite work. The
 by Nisan Stiennon on Logical counterfactuals and differential privacy | 0 likes

I at first didn't understand
 by Sam Eisenstat on An Untrollable Mathematician | 1 like

This is somewhat related to
 by Vadim Kosoy on The set of Logical Inductors is not Convex | 0 likes

This uses logical inductors
 by Abram Demski on The set of Logical Inductors is not Convex | 0 likes

Nice writeup. Is one-boxing
 by Tom Everitt on Smoking Lesion Steelman II | 0 likes

Hi Alex! The definition of
 by Vadim Kosoy on Delegative Inverse Reinforcement Learning | 0 likes

A summary that might be
 by Alex Appel on Delegative Inverse Reinforcement Learning | 1 like

I don't believe that
 by Alex Appel on Delegative Inverse Reinforcement Learning | 0 likes

This is exactly the sort of
 by Stuart Armstrong on Being legible to other agents by committing to usi... | 0 likes