That would depend on the terms of contract, so it could be way more than 3.6B. There may not even be a contractual clause for a buyback.
Activision had a publishing deal with Bungie. They didn't own them.
For Bungie to get freedom again they need to buy themselves back off Sony like they did with Microsoft. That's 3.6 billion.
What do you think Sony gave 3.6 billion for? Bungie is now answerable to SIE who are answerable to Sony.
The terms of the contract are that Sony bought the 100% shares of Bungie and that it's now a fully owned SIE subsidiary. They didn't mention any clause to buyback and I don't know a single example of any company that had it. Sony bought it and it's now fully integrated inside SIE. Bungie is not an independent company anymore: now it's a fully owned Sony/SIE subsidiary.
The "freedom" they got is that they will continue publishing under the Bungie publishing label (not the PS Studios one) in rival consoles and PC releasing their new games there day one (maybe because Sony wants to keep the PS Studios label for games and IPs that day one only release on PS, and that never release on other consoles), and like the other teams from PS Studios they have creative freedom.
3.7B is a ton of money for one (I think they are two) game development studio with a single IP. But that IP has the record of best selling new IP ever and meant a revolution for GaaS, MP and FPS in console and before that they also created another top IP that also meant a revolution for console MP and FPS. They are top tier new IP creators, top tier GaaS makers and top tier FPS and MP devs. Sony didn't have top tier GaaS, MP or FPS and now they have, and also got top tier new IP creators and a top IP published and at least a couple of new IPs -that I assume Sony saw and feels very confident about them- to be released in 2-3 years or so. And well, Bungie makes a lot of money so it's extra revenue and profit to add on top of the SIE one.
Do what they like with new games I just hope this isn't the rebirth of platform exclusive strikes and exotics. Think bungie came out and said they won't do that again but you never know.
Would love to see a new single player shooter from them but I assume Sony gonna want a Live service game. Nothing out there feels as good as destiny's shooting so big win for Sony.
They said they want the same experience for players in all platforms for current and future Bungie games: games will be released day one everywere with no platform exclusive content or different experience. This means that if Sony gets someting exclusive it would be betas/demos, bundles, marketing or inclusion in game subs.
Regarding single player, I think all Bungie games always had single player campaign and I don't see any reason of why it would change in the future games. But pretty likely yes, their main focus will be multiplayer even if coop.
I don't think Sony cares if Bungies games are multiplat. They get the revenue, and they didn't buy Bungie for their IP, they bought them for their expertise. Bungie will be massive in helping other Studios build their GaaS experiences.
One of the Sony goals is to monetize better non-PS gamers. PS has 100M+ players, consoles have between 200M+ players and there are like 3B players out there. Which means there are leaving a ton of money on the table if they stick to consoles or particularly PS.
The other consoles don't add much, for Sony makes more sense to grow specially in PC and mobile. So it's a great move for Sony to have PS Studios and 3rd party deals to feed their consoles with exclusives and control the console market, but also own other publishers separated from PS Studios that monetize players that are not only in PS, but also in the other consoles and specially PC and mobile.
So condidering that strategy, it makes sense to buy Bungie -and potentially more publishers in the future- and keep them to release their games day one everywhere. I assume that from these acquired multiplatform publishers they'll only keep exclusive for themselves marketing, betas/demos, bundles, movies/anime/tv shows, potential VR content and in a few rare cases some (often timed) console exclusives. And their revenue/profit, obviously.