3 ms·
Depends what you mean by unilateral. You can have a Nash equilibrium and also implicit collusion, for example if one player is playing GTO, that is they are pla
by Kranar 3y ago
Depends what you mean by unilateral. You can have a Nash equilibrium and also implicit collusion, for example if one player is playing GTO, that is they are playing optimally under the assumption that all other players are acting independently, and two other players are implicitly colluding with one another, you can still have a Nash equilibrium so that none of the players stand to gain anything by changing their strategy, and also the player playing GTO will have a negative expected value.
Imagine a situation where the collusion was explicit, you are playing GTO against two opponents who are colluding with one another. A Nash equilibrium will still exist in that situation but your EV will be negative. Now explicit collusion is considered cheating but you can imagine a scenario where two players play in such a way that even though they are not explicitly colluding with one another, they behave the exact same way as if they were. This happens among a group of loose players where their actions as a group rewards the group as a whole against players who are acting independently.
In other words, just because a strategy is optimal does not mean that it results in a positive expectation. You might be in a situation where playing perfectly just minimizes your losses, but you will still lose anyways.