Near the end of his life, he was back in the US. Thought he was being shadowed. Took therapy, medicine, treatment for hypertention.
Years later, it turned out that he was being shadowed. The man was working on his mental health, confirmed by doctors to be paranoia. The FBI was shadowing him because of his work in cuba.
During pre-colonial times, the French and the British went over to America. Their domains overlapped on the Canadian border where the Iroquois nation (actual emphasis on "nation") lived, and a three way war began between the three nations, since the British wanted to spread itself (because did you expect anything else from them) and the French were trying to establish outposts while the Iroquois didn't like intrusion on what it considered to be a neat system it built, even though they didn't have as much issue with the actual missions.
The Iroquois, believe it or not, were champion warriors and pretty much wiping the floor against both of them until thirteen of the twenty colonies (yes, there were twenty colonies, not thirteen) started to rise up, and the British sided with the natives they realized were the powerhouse they were. The only issue is those natives were still susceptible to internal strife which allowed the to-be United States to win and take Upstate New York (which was the Iroquois homeland, and yes, the border between the conquered parts of New York and the parts that were in the state precolonially would objectively be the most correct line to mark where Downstate officially ends) and Vermont (which was claimed by the Iroquois but never formal territory). The British, having lost, left the area and gave the natives the cold shoulder because the natives were still viewed as barbarians, even up to the establishment of the league of nations hundreds of years later where those natives were denied membership (since the Iroquois rump state in exile still exists).
Of note, I really shouldn't be calling them the Iroquois (their name was the Haudenosaunee), Iroqu was the Algonquin word for "serpent" (the Algonquins were like the Russia to the Haudenosaunee's Ukraine) and was a slur the French unknowingly picked up and popularized/coined, but very few people would connect the dots if I just referred to them as the Haudenosaunee.
A lot of multiparty civil wars have different sides with mutually exclusive goals.
If you want to talk about boardgames, there are games like Root where different factions have their own separate rules that conflict with allowing multiple people being able to win.
What was a time that two adversaries had such different objectives...
Then, would they be adversaries in any meaningful way? I mean, fighting against someone means both must be competing for the... same objective, resources, whatever. If they aren't they aren't competing.
In chess there is a fairly common situation where you are in first place in the last round of a tournament, 1/2 of a point ahead of your opponent (you get 1 point for winning a game and 1/2 point for a draw). So if you win or draw the game, you win the tournament and get a lot of money. If you lose the game, your opponent wins the tournament and gets the money. You get 2nd place, i.e. less money possibly split with other competitors.
That means you can choose a safe playing strategy that likely leads to a draw, while your opponent has to choose a risky strategy with higher chances of winning.
(Some chess context: high level games are usually drawn. They are only won by someone making a mistake. Also, the first move (white pieces) confers an advantage, so it's usual to seek winning opportunities if you have white, while just trying to hold the draw if you have black. To attempt winning with black requires seriously risky play. Bobby Fischer basically conquered chess in the 1960's by constantly trying to do that, which required playing with maniacal intensity all the time).
I get that but, no matter their strategy, aren't they still competing against one another for the same resources: a (better) ranking in the leaderboard?
Replying to myself, in the hope of being read by the people downvoting my first comment: you realize silently downvoting doesn't help me understand the slightest why you disagree with what I wrote and where I may be mistaken, right?
I didn't downvote you, I think you offered a thoughtful critique of the question.
Even if parties have wildly different objectives or winning conditions, if they didn't have to compete for the same resources then they could cooperate or at least ignore each other. That wouldn't be true if it were a race to finish first, but in that case they've started competing for the resource of time.
Maybe some folks thought it was a cop out answer, since I was seeking new perspectives rather than a reason to not ask for them? But, I think your response can help guide responses to even more extreme examples than some potentially topical ones by taking you up on your challenge.