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$\textrm{Exp}^{\textrm{ind-mode}}_{\mathcal{FE},A}$ is just the name given to the interaction. The "exponent" $\textrm{ind-mode}$ is part of that name. There is not really a standard, universal way of giving names to these kinds of games. But usually the author has to specify: what game is it? what scheme is being attacked? what is the attacker? ...

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