I can't see how a 4 player game cannot go but one way, every time, if the following (rational) rule applies:
You attack whoever is weaker than you but poses a threat.
So you have four players. All roughly equal strength (normal distribution, variance proportional to time). The following sequence occurs:
- Player A becomes stronger than another (B)
- Player A attacks B because they are likely to win.
- Player B is defeated (-10 strength), but player A is also weaker due to attacking and unable to defend simultaneously (-5).
- Player C is now stronger than A, so they attack.
- Player A is defeated (-10 strength), but player C is also weaker due to attacking, but less so because player A was already weakened, so -3 strength for player C.
- Player D is now strongest, and attacks the next strongest player, C.
- Player C (likely) loses, player D is now most likely to be victorious.
Basically, whoever attacks first starts a cascade of attacks, A->B, C->A, D->C, where the greatest advantage is to whoever attacks later, or latest, after everyone else is done weakening each other. And whoever attacks first is most disadvantaged overall.
Unless some massive swing of luck where someone can beat the odds stacked against them, or some alliance mechanics are introduced, how can the game possibly deviate from this pattern, if only for exceptional cases? Other than relying on people making irrational decisions (attacking someone stronger, or someone not a threat to their victory)
I believe this is a more general 4 way zero-sum game problem, but Eclipse is the example I'm thinking of.
Edit: I think this bit of game theory, about 3 way duels, basically proves there's only one optimal way to play Eclipse FFA. Don't play. https://en.wikipedia.org/wiki/Truel