[StellarWind]

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Yes, and no. If player A departs from the equilibrium strategy in such a way that an "innocent" player (B) is in a "negative EV situation", then by definition, B has a different strategy they could follow that would be better than the equilibrium strategy they were originally following, and so can obtain a non-negative EV - this shifts the negative EV to some other "innocent", who can also switch to a better strategy, and so on.

Ultimately, all of the players can (in theory) switch strategies so that the negative EV falls back on the player who's playing a non-equilibrium strategy. The other players may not be able to guarantee a positive EV in their new equilibrium, but they can at least remain non-negative.

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This is not correct. If player A deviates from the equilibrium strategy in a multiplayer poker game then player B may be screwed. He may have no strategy that avoids negative EV. Players A and B both lose and the other players gain.

I believe I gave some valid poker examples of this in my last post, but poker is complicated and proof can be elusive.

Here is a non-poker example that illustrates my point. Three players play a game in which each player antes $1. The first player chooses a whole number between one and three and annouces it out loud. Then the second player chooses a number between one and three and announces it out loud. Finally the last player chooses his number. Choosing duplicate numbers is allowed.

Now a "3-sided die" is rolled to generate a random number between 1 and 3. Each player who chose that number gets an equal share of the pot. If no one picked the number the game is a chop and the antes are returned.

Clearly it is bad to have the same number as someone else. Optimal strategy for each player is to pick a number that no one else has picked yet. This is also the Nash Equilibrium strategy for all players and it yields EV=0 for each player if everyone follows it.

I'm player "A". Whenever I am second to act my strategy is to choose the same number announced by player B sitting on my right. This is a really bad strategy and it is going to cost me a lot of money. But notice that Player B has the same EV as I do. He's played perfectly but he is no better off than I am and there is nothing he can do to improve his situation. We're both losing money to player C on my left.