12:1 Therefore, since we are surrounded by such a great cloud of witnesses, we must get rid of every weight and the sin that clings so closely, and run with endurance the race set out for us, 12:2 keeping our eyes fixed on Jesus, the pioneer and perfecter of our faith. For the joy set out for him he endured the cross, disregarding its shame, and has taken his seat at the right hand of the throne of God.

The question to be explored here concerns the correct translation of the preposition ‘anti‘ (‘for’).  It can be translated in two different ways:

(a) ‘Because of; for the purpose of’.  Jesus was willing to endure the pain and shame of the cross because of the joy that awaited him after his suffering.  This reflects the most common translation of the present verse.  More generally, however, it is an uncommon meaning, although it does occur in Eph 5:31 – ‘For this reason (ἀντὶ τούτου) a man will leave his father and mother and be united to his wife.’

O’Brien: The only other occurrence of ‘anti’ in Hebrews is in Heb 12:16, where it clearly means ‘in order to obtain’.  The prospective joy of Jesus’ exaltation is a frequent theme in Hebrews, and ndeed is mentioned in the following words, ‘sat down at the right hand of the throne of God’.  The athletic idiom in this passage suggests that this joy was the winner’s prize that was set before Jesus.  In context, the future joy set before Jesus encourages struggling believers to await a similar reward.  This prospective joy is consistent with the encouragement of Heb 10:35 (‘do not throw away your confidence, because it has great reward’), and the idea of faith set out in ch. 11 (‘the substance of things hoped for’).

This interpretation is also supported by Ellingworth, Michaels, Gundry, Hughes, Peterson, Thompson and others.

(b) ‘Instead of; rather than’.  This reflects the most common meaning of ‘anti’, but a less common translation of the current verse.  Cf. the NLT footnote: ‘instead of the joy…’

Lane: Considerations of context favour ‘rather than (the joy)’.  This ‘joy’ which was renounced by Jesus, could have been his heavenly status (Phil 2:6–7; 2 Cor 8:9; cf. Heb 11:24-26).

This interpretation is supported by Calvin, Murray Harris, and a few others.

I find it difficult to adjudicate between these two interpretations.  I slightly lean towards (a).  The difference, though real, is not critical, since both can be defended theologically, and by appeal to other passages of Scripture.

See also this, by Bill Mounce.