That's a helpful example, and in line with what I've been thinking about Adventurers League. If I understand your purpose properly, you are not counting on Gygax's particular authority as an original designer of the game, and using him only as an example DM.
Correct.
A question it raises is on what grounds do I say "the game" has persisted? First of all, one must say in what form does "the game" exist at all? I've claimed that it exists only while played. That view fits with my claims elsewhere that game-as-artifact is a tool for fabricating game-as-played. The artifacts I have in mind would include dice, rulebooks, maps of Greyhawk, DM notes and player character sheets. Although it might be an unfamiliar and rather objective way to put it, I would count the imagination of each participant among artifacts necessary to play a TTRPG.
There is the ongoing set of players contributing to the campaign setting by their actions. The DM is also contributing to the campaign setting and he can do that at any time even with or without players. The obvious intent of course is for players to experience it at some point but it doesn't have to be inside a session. For example, I would work out a plot in my world where the King of one of my kingdoms is overthrown by treachery and a new King is on the throne. When a new group shows up to play that is established fact in the world they are playing. I'd argue the campaign begins when the DM starts creating the history in prep for his first session.
I think for me there are assumptions that perhaps many don't hold. One is the DM can get a group whenever he wants. If you are a good DM in a reasonably populated area this is true. Second, that some DM's run a continuing campaign. That was what Gygax did so I don't find it that hard. I ran two groups at once in the same campaign world. They didn't meet until high levels. Where those two separate campaigns or one with two groups of players. I'd say one.
What I have been referring to as "the game" all through, is the game as played. So the first question is to ask whether that is what you are referring to? It seems possible that what you're observing is that Gygax continues to own some artifacts that were used to fabricate "the game". You could then be saying that whatever game is fabricated in future with a new set of players will look enough like what was fabricated in the past with the now-departed cohort, that you're prepared to call it the same game.
Yes assuming it's the same campaign perhaps advanced a little in time. The effects of the old PCs could be discovered by the new PCs. Not every DM does that sort of thing. I don't do it all the time. I love world building so I will do a brand new campaign. To me the campaign is the setting with a continuing history. So can DMs have more than one campaign, yes. Does the number of groups equate to the number of campaigns? No. It could still be one campaign or it could be as high as the number of groups where each had a unique setting.
If that is right, then I can make the same claim on behalf of the now-departed cohort given only that they create continuity with "the game" represented on their character sheets and in in their imaginations. One might say - "Let's meet on Tuesday night to continue our Greyhawk campaign." Gygax can say that they're not playing "the game" that they were playing in the past, because his imagination is no longer available to them. And they can mirror that claim right back, because their imaginations are no longer available to him.
Yes. I would agree with Gygax. Even if they play in same "purchasable setting" like the World of Greyhawk, there is so much fiction that the DM has contributed on camera but more importantly off camera. There may be an assassin whose been tracking the party for months which they knew nothing about but the DM did. But in contrast, the DM knows of all the PC contributions to the fiction in his campaign. If the DM didn't run it or authorize it, it didn't happen.
A long while ago on these boards I claimed that the game played is distinct to each cohort of players, such that it is better to picture multiple versions of the game... one for each cohort. The versions can bear a very close family resemblance, but they are not utterly identical. That seems very obviously the case where groups disagree on the meaning of rules, for which examples abound on Enworld.
For me, a campaign represents a snaphot of the rules most of the time though I admit when editions changed some campaigns survive the change. But most of the time, if I decided for flavor reasons to establish some houserules those would hold for that campaign but perhaps not every campaign.
In conclusion, I would resist the claim to high ground you seem to be making by changing the sentence I bolded to read "All versions are new games based on their new participants." One response I can think of is to say "Very well, there are multiple versions of the game, but I count DM's version superior to that of the players". Which begs the question: why? The preferencing is a norm one can tacitly opt into, a fact about ones attitudes rather than an ontological fact about games.
It's not a matter of superiority other than superiority of knowledge. The DM knows the campaign setting in ways the PCs can never know it. Even if they spend 20 levels their they will have barely scratched everything the DM would know. The DM is the possessor of the knowledge. If a group rejects a DM, and I agree some are worth rejecting, then they reject the campaign. The DMs actions and their campaign are often fused together.
I'm just saying that playing in a world passingly resembling another DMs is not the same thing. I've never played in one of Gygax's campaigns even though I have played in Greyhawk. Unless you've had Gygax as DM.
