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Dative: goal as satellite
οἳ δ᾽ οὔ πω πείθοντο, λόχῳ δ᾽ ὑπεθωρήσσοντο
‘They did not believe him, and armed themselves for an ambush.’ (Hom. Il. 18.513)
Sometimes the dative signals a satellite or goal in the case of abstract nouns which indicate a situation, mainly in Attic inscriptions.
Historical background
Since some forms of the infinitive (specifically the suffix -σθαι) continue old datives, the use of this type of infinitive as an adverbial of goal could, from a historical perspective, be regarded as a dative of goal.
ἐγὼ ταῦτα ἔπρηξα τῇ σῇ μὲν εὐδαιμονίῃ, τῇ ἐμεωυτοῦ δὲ κακοδαιμονίῃ
I have done this to your happiness and to my own misfortune. [provisional translation]
ἀλλὰ γὰρ ἤδη ὥρα ἀπιέναι, ἐμοὶ μὲν ἀποθανουμένῳ, ὑμῖν δὲ βιωσομένοις
But now it is time to leave: I to die and you to live. ֍