Eclipse 4 player FFA Convergent Strategy

Question

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:

1. Player A becomes stronger than another (B)
2. Player A attacks B because they are likely to win.
3. Player B is defeated (-10 strength), but player A is also weaker due to attacking and unable to defend simultaneously (-5).
4. Player C is now stronger than A, so they attack.
5. 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.
6. Player D is now strongest, and attacks the next strongest player, C.
7. 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

Answer 1

In the pattern you propose, players A, B, and C all come out losing, and given what you propose, they should have known they would come out losing. Thus, they didn't make the best choice for them.

It is true that Eclipse, unlike most Eurogames I've played, rewards attacking weaker players, as opposed to encouraging you to go after the person in the lead to prevent him from winning. However, there are a few things that players could have done differently in your scenario:

1. Build up more. A shouldn't have attacked B when he did. If he knew that this would leave him weaker than C and thus be attacked by C, then he shouldn't have done it. Instead, he could have continued to build up, to a point where attacking B wouldn't weaken him when he does.

   One way to do this is to rely on missiles instead of cannons. This tends to be very strong in the base game anyway. But when you win with missiles, you walk away as strong as you were when you went into the battle; rather than both sides taking casualties.

   In games I've played, often attacking doesn't happen until the last several rounds. The beginning of the game is all about building up, and attacking only ancient ships that you are pretty sure you can beat without losses.

2. Teaming up. In the Rise of the Ancients expansion, you can officially team up, but even without that you can make alliances. If A was the strongest, then B, C, and D could have worked together to go after him. While you can't actually team up in a given battle, each player could attack a different one of A's territories, leaving him unable to defend them all.

3. Take chances. It doesn't require a "massive swing of luck" to defeat an opponent that has better odds than you do. Sometimes a better opponent may just have a 60% chance of winning. Even though you wouldn't generally attack someone in that position, there are times when taking that 40% chance of victory is your best hope at winning the game.

   Similarly, on the other side, don't automatically attack someone just because the odds are in your favor. Even if you have a 75% chance of winning, often the penalty for losing will be enough that it's not worth the risk.

4. Rock-Paper-Scissors. This isn't a strategy to follow, but just a fact about the game. It is not always the case that just because A is stronger than B, and B is stronger than C, that A is stronger than C. A may be strong against things that B has, but weak against things that C has. This is especially true of things like missiles vs extra hulls. Consider this situation:

   Player A has missiles and no extra hulls or cannons.

   Player B has lots of cannons and a few extra hulls.

   Player C has many hulls and a single cannon.

   Here, A will usually defeat B. B will usually defeat C. And C will usually defeat A.

   This shows that you can's simply order players in order of strongest to weakest.