In a two$-$person zero$-$sum game, all pure equilibria have exactly the same payoffs for Row $($and hence for Col as well$).$ Consider a $3-$person zero$-$sum game, with players A$,$ B and C$.$

If two profiles $($A$,$ B$,$ C$)$ and $($A$,$ B$,$ C$)$ represent pure equilibria, must the payoffs to each player be the same in each of these equilibria?

$($Clarification: the question is whether A must receive the same payoff in both equilibria, and similarly for players B and C$.$ The payoffs can be different for the different players.$)$