ἀντὶ παίδων ... ἱκετεύομεν here=“πρὸς παίδων”, “"by them,"” i.e. “"as you love them,"” a very rare use of ἀντί, but one which comes easily from its ordinary sense, “"in return for,"” “"as an equivalent for."” It would be as much as their lives are worth to refuse the prayer. (In El. 537 “ἀντ᾽ ἀδελφοῦ” is sometimes taken as=“"for his sake,"” but this is by no means certain.)
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