[LINK] EdTech startup hosts AI Hunger Games (cash prize $1k)

If there is a third kind of player, which cooperates on the first round and then slacks thereafter, then the third group will blow the second out of the water. The second group only wins because no one bothered exploiting them in your example, even though anyone easily could have.

If there are two kinds of players, those who throw rock, and those who throw paper, the latter will blow the former out of the the water.

You are engaging in two fallacies: you are cherry-picking conditions to favor your particular strategy, and you are evaluating the strategies at the wrong level. Strategies should be evaluated with respect to how the affect the success of the individual person employing them, not on how they affect the success of people, in general, who employ them. This fallacy is behind much of the cooperate/one-box arguments. Sure, if everyone in Group B cooperates with other members of Group B, then Group B will do better, and on a superficial level, it seems like this means "If you're in Group B, you should cooperate with other members of Group B", but that's fallacious reasoning. It's the sort of thing that lies behind identity politics. "If Americans buy American, then Americans will do better, and you're an American, so you will benefit from buying American". Even if we grant that buying American gives a net benefit to America (which is a rather flimsy premise to begin with), it doesn't follow that any American has a rational reason to buy American. In your scenario, the presence of people with the "cooperate with people who have a reputation greater than 0" provides a reason to cooperate in the first round, but there is no reason whatsoever to condition cooperation on someone having a reputation greater than 0. Anyone who, in this scenario, thinks that one should cooperate with people with reputation greater than 0 does indeed not understand game theory.

From the FAQ

Q: "Is it allowed or disallowed to collude with other algorithms (potentially your other submissions, submissions of your friends, etc.) based on agreements outside the game? (e.g. make 1 out of 100 a 'winner' and have the other 99 just help this chosen winner)"

A: "Collusion based on agreements outside the game will result in disqualification. If however, your algorithm is smart enough to determine in game that another algorithm is signaling and you wish to respond in a cooperative manner, i.e. collude, this is allowed as it is, by definition, part of the game."

Then this game actually seems to be about getting strategy data out of reputation data. The zeroth-level strategy is to defect very time, because that's the nash equilibrium. An example of a first-level strategy is to cooperate against players with reputation higher than some cutoff, and defect against everyone else, because you want to coooperate against cooperaters to outlast the slackers. A second level strategy models the other players modeling you, so you might for example cooperate against players with reputation higher than some function of your own reputation.

So I think the way to go in an idealized version of this game is to model other players as simple third-level players and try to predict whether they'll cooperate with you, based on reputation and the past reputation matrices, and picking a strategy to maximize food over future rounds, which means keeping a reputation where the backlash from slacking has yet to outweigh the food gained form it.

But there are some non-idealities. As the game goes on, reputation varies more slowly, so you can actually start playing tit-for-tat strategies - and so can other people. Identifiability, and most of the slackers getting eliminated, increase the costs for defecting. Of course, you can test whether people have identified you or not by defecting against unknown-strategy players occasionally and seeing if they tit for tat you back. If they don't, then you can model them as third level players and not have to treat them as equals.

Dealing with the random factor m is a lot like the iterated prisoner's dilemma - you cooperate the first time or two, then can go to tit for tat. Which is to say, you start out by being more likely to cooperate when m will take cooperation to reach. Bu if other players don't reciprocate enough to make it worthwhile, you just ignore m. It's good for cleverer players if the goals are reached, though, because it keeps the slackers and exploitable players in the game, which is a source of relative advantage for cleverer players.