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I was thinking, in melee it is impossible to 'starve' your enemies of points by being a perfect dodger, because they can just shoot other people. The scoring isn't done on how much bullet damage they get against *you*, but against everybody, cumulatively. So getting a good dodging movement doesn't help as much in melee as it would in 1v1.

In fact, in melee the only way to improve your score is to boost your own bullet damage and survival. And what better way to do this than to move aggressively, with some sort of wavesurfing-derived movement? That way you get the dodging at close distances so you live long enough to survive, while feeding off of bots which aren't capable of dodging at close distances because they just want to run away. So you get high hitrates, which boosts your bullet damage and you get energy bonuses which keep you alive. By making sure that you are scanning them when their gunheat is cool you know that you can catch all of their waves, and when their gunheat is high you can scan around to make sure nobody is sneaking up behind you.

Thoughts?

Makes sense. It is a very simple case (the only one I have looked at ...) but it is instructive how well DoctorBob scores in the nano melee. The best defensive bots do a little better, but its aggressive strategy has held a strong third for many years.

Yep, this is a very valid strategy, at least until there are 4 bots left. In the beginning of a round a lot of bots behave like panic, don't know where to go, don't know where to shoot. That is the time to be aggressive and score your bullet damage and up your energy level. But when you're down to 4 (or 5) bots it is time to hold your horses and change the strategy. Although cornering an opponent is a good idea, the journey to the corner will probably be fatal to you. Even in higher weightclasses DoctorBob plays a good game, with a relatively high bullet damage. Its survival is also ok, but he hardly ever reaches the last 3 because his strategy fails at that point (but what do you expect from a nano).
I would like to see a 'micro-DoctorBob' with a secundary strategy for the endgame, although its gun would probably not be very effective at larger distances.

As a side-note: To some extend Gruwel is using such a strategy. Although not as agressive as DoctorBob, it certainly does not flee and (tries to) take out everybody near it. In the endgame it starts shooting peas (distance-dependent) to try to boost survival.

I think the kind of strategy you are describing has already been used very effectively by Wallaby.

Do you have any idea why DoctorBob is so successful while other aggressive nano melee bots aren't?

Many melee bots use convenience targeting (aim at the closest opponent). Because of that, the dominant strategy for over a decade has been to stay away from everyone to avoid being targeted. If no one is shooting at you, you effectively have 100% dodging and perfect survival. And survival score counts a lot in melee (each bot you outlast means extra 50 points).

Which is the highest ranked melee bot which doesn't use either Minimum risk or Anti-Gravity Movement?

But in teamrumble, then it is a completely different story. There are 2 aggressive movement teams in the top 5. If there is a single melee bot ramming against you, shoot power 3 bullets and it is toast. If there are 3 team bots ramming against you, you're toast.

I presume you, as a game theorist, know about the Prisoner's dilemma (probably more than I do). Do you think melee bots will ever be smart enough to cooperate and form temporary teams? Or would communication be too difficult?

I'm initially skeptical it would be advantageous. Against the weaker bots, you'd only be able to eek out a small amount of extra score, while against the stronger bots you're temporarily teaming up with, you have a lot of room to gain points by killing them instead. (E.g., going from 50% to 55% is a lot easier than going from 94.9% to 99.9%.)

But upon further thought, if two top bots already know they'll get about 50% against each other whether they team up or not, why not save that battle until the end and maximize the score vs everyone else by killing them all first. I don't really see it ever happening, but maybe it could be viable.

Edit: Using the terms from the Wikipedia article, I'm trying to say that I'm not sure R > P. You may have relatively little to gain by maximizing score vs the weak bots, and you have much to gain by improving score vs the other strong bot. For the weaker bot, of course it's advantageous to team up, but it may never be for the stronger bot. (I'm also presuming that any bots trying this would be the strongest bots, which I think is likely.) (And of course this is all complicated by differing performance in Melee vs 1v1, too - teaming up with Diamond and then facing him 1v1 every round might be a bad idea.)

I know about prisoners dilemma. I also know about trigger strategies and sustained collusion.

Meleerumble is not a prisoner's dilemma. It is a constant-sum game (all bots scores always sums 100%), while prisoner's dilemma is not. In constant-sum games, collusion is never sustained.

But 2 player sub-games do have prisoner's dilemma aspects. If 2 bots collude, they both increase their chances of survival against the other 8. If 2 bots shoot against each other, they both diminish their chances of survival. If one shoots but the other not, the one shooting gains an advantage (earning points and gaining energy).

Don't expect existing bots to learn collusion as most bots have no active developers looking after them. The rumble is full of hardcore defectors and hardcore cooperators, and in prisoner's dilemma, the best response against hardcore players who pick the same strategy regardless of what others are doing is to defect against them as well.

For collusion to work, even temporary, at least 2 bots need to go for it. If you upload a single trigger strategy bot, it won't work. If you upload a bunch of trigger strategy bots, like 300, then it might work.