are the two players physically precisely the same (including environment), at least insofar as the players can tell?
In the examples I gave yes. Because thats the case where we have a guarantee of equal policy, from which people try to generalize. If we say players can see their number, then the twins in the prisoners dilemma needn’t play the same way either.
But this is one reason why correlated equilibria are, usually, a better abstraction than Nash equilibria.
The “signals” players receive for correlated equilibria are already semantic. So I’m suspicious that they are better by calling on our intuition more to be used, with the implied risks. For example I remember reading about a result to the effect that correlated equilibria are easier to learn. This is not something we would expect from your explanation of the differences: If we explicitly added something (like the signals) into the game, it would generally get more complicated.
The “signals” players receive for correlated equilibria are already semantic. So I’m suspicious that they are better by calling on our intuition more to be used, with the implied risks. For example I remember reading about a result to the effect that correlated equilibria are easier to learn. This is not something we would expect from your explanation of the differences: If we explicitly added something (like the signals) into the game, it would generally get more complicated.
It’s not something we would naively expect, but it does further speak in favor of CE, yes?
In particular, if you look at those learnability results, it turns out that the “external signal” which the agents are using to correlate their actions is the play history itself. IE, they are only using information which must be available to learning agents (granted, sufficiently forgetful learning agents might forget the history; however, I do not think the learnability results actually rely on any detailed memory of the history—the result still holds with very simple agents who only remember a few parameters, with no explicit episodic memory (unlike, eg, tit-for-tat).
In the examples I gave yes. Because thats the case where we have a guarantee of equal policy, from which people try to generalize. If we say players can see their number, then the twins in the prisoners dilemma needn’t play the same way either.
The “signals” players receive for correlated equilibria are already semantic. So I’m suspicious that they are better by calling on our intuition more to be used, with the implied risks. For example I remember reading about a result to the effect that correlated equilibria are easier to learn. This is not something we would expect from your explanation of the differences: If we explicitly added something (like the signals) into the game, it would generally get more complicated.
It’s not something we would naively expect, but it does further speak in favor of CE, yes?
In particular, if you look at those learnability results, it turns out that the “external signal” which the agents are using to correlate their actions is the play history itself. IE, they are only using information which must be available to learning agents (granted, sufficiently forgetful learning agents might forget the history; however, I do not think the learnability results actually rely on any detailed memory of the history—the result still holds with very simple agents who only remember a few parameters, with no explicit episodic memory (unlike, eg, tit-for-tat).