= Symmetry of players in a cooperative game
{title2=$v(S\cup\{i\})=v(S\cup\{j\})\quad(S\subseteq N\setminus\{i,j\})$}
Players $i,j$ are symmetric when interchanging them does not affect any <coalition> value. The displayed condition is equivalent to invariance under their transposition. If every pair is symmetric, arbitrary permutations preserve the game, and <coalitions> of equal <cardinality> have equal values. This is a property of the <transferable utility game>, rather than a requirement that a chosen <payoff> allocation treat players equally.
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