by Jessica Taylor 923 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.

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