I'm hoping some game theorists will chime in here; it doesn't matter if you don't get macro. I need your help, and want your thoughts on my intuitions:

**Not all Nash equilibria are created equal.**

**Game A**. There are n identical players who move simultaneously. Player i chooses Si to minimise a loss function Li = (Si-Sbar)^{2} + (Si-Sbar)(Sbar-S*), where Sbar is defined as the mean Si over all players, and S* is a parameter that is common knowledge to all players.

This game has a unique Nash equilibrium Si = Sbar = S*.

**Game B** is exactly the same as game A, except the loss function is now Li = (Si-Sbar)^{2} + (Si-Sbar)(S*-Sbar). (I flipped the sign of the last bracketed term.)

This game also has a unique Nash equilibrium Si = Sbar = S*.

I think the Nash equilibrium in game A is plausible, but the Nash equilibrium in game B is implausible.

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