Melbourne's Hamer Hall and Sydney Opera House are considering collaborating to bring the Vienna Philharmonic Orchestra out to Australia. The Orchestra has a set price schedule for overseas tours, so the fee schedule is not negotiable. The Orchestra's fee to come to Australia for two weeks is $4m and their fee to come for one week is $3m. They can perform at up to 2 venues on a trip and each venue would be allocated either one week or two.

The Orchestra is only available from 17-30 January of 2022. Both Melbourne and Sydney would prefer to have the Orchestra come later in January, because many people are away earlier in January and concerts are poorly attended. The following table indicates their calculated earnings from various options, before deducting the cost of booking the Orchestra:

	Melbourne's Hamer Hall	Sydney Opera House
Melbourne first week, Sydney second week	$1m	$8.5m
Sydney first week, Melbourne second week	$2.5m	$8m
Melbourne whole period	$3m
Sydney whole period		$9.5m
Melbourne only second week	$2.5m
Sydney only second week		$8.5m

(You do not need to consider any other options than the ones in the table.)

What is Hamer Hall's BATNA?

What is Sydney Opera House's BATNA?

Do Hamer Hall and the Sydney Opera House agree to have the Orchestra come to two venues? If so, which venue has the Orchestra first?