The two examples differ in games between B, C, and D, which don’t involve A at all. So I don’t see a problem: even though A has done better in the second example, B and C have improved more, so they win instead. You can construct something similar in a round-robin chess tournament, where you can win one tournament with a lower score than another tournament you lost.
Can you construct an example where only games involving A are changed?
This is a highly artificial example, but consider the following...
Case 1: A mutually defects against B, and mutually defects against N other bots. B mutually defects with those bots too. Assume the N bots defect among themselves. The contest is a draw.
Case 2: A cooperates with B, who defects. A mutually cooperates with the N other bots. And of course, B still mutually defects against those N bots.
For sufficiently large utilities of the (D, C) outcome, in this case B would win the contest, even though A got an improved score by cooperating with those other N bots (minus a small penalty for getting (C, D) instead of (D, D) against B).
Oh, I think I see. In a conventional tournament setting, the same idea can apply: if B beats C and A can beat exactly one of them, it’s better to win against B and lose against C rather than vice versa.
This doesn’t usually come up in conventional tournaments because winning is believed to be transitive: making yourself a better player makes you more likely to beat both B and C. Here, on the other hand, there may be trade-offs. For example, it’s probably worthwhile to use a trick that achieves (D,C) against ReallySmartBot if it requires mutually cooperating with CooperateBot, rather than cooperating with the former and exploiting the latter: ReallySmartBot is a dangerous competitor and CooperateBot probably isn’t.
I don’t actually see a way to take this into account in the current metagame setting. But this could be an interesting thing to think about after we know the results.
I guess it bothers me that in the current metagame all the contestants are aiming to win, rather than to maximize their score (except for the ones who are just aiming to troll the rest of us by submitting humorous bots). In that sense the situation is not really a true prisoner’s dilemma.
The two examples differ in games between B, C, and D, which don’t involve A at all. So I don’t see a problem: even though A has done better in the second example, B and C have improved more, so they win instead. You can construct something similar in a round-robin chess tournament, where you can win one tournament with a lower score than another tournament you lost.
Can you construct an example where only games involving A are changed?
This is a highly artificial example, but consider the following...
Case 1: A mutually defects against B, and mutually defects against N other bots. B mutually defects with those bots too. Assume the N bots defect among themselves. The contest is a draw.
Case 2: A cooperates with B, who defects. A mutually cooperates with the N other bots. And of course, B still mutually defects against those N bots.
For sufficiently large utilities of the (D, C) outcome, in this case B would win the contest, even though A got an improved score by cooperating with those other N bots (minus a small penalty for getting (C, D) instead of (D, D) against B).
Oh, I think I see. In a conventional tournament setting, the same idea can apply: if B beats C and A can beat exactly one of them, it’s better to win against B and lose against C rather than vice versa.
This doesn’t usually come up in conventional tournaments because winning is believed to be transitive: making yourself a better player makes you more likely to beat both B and C. Here, on the other hand, there may be trade-offs. For example, it’s probably worthwhile to use a trick that achieves (D,C) against ReallySmartBot if it requires mutually cooperating with CooperateBot, rather than cooperating with the former and exploiting the latter: ReallySmartBot is a dangerous competitor and CooperateBot probably isn’t.
I don’t actually see a way to take this into account in the current metagame setting. But this could be an interesting thing to think about after we know the results.
I guess it bothers me that in the current metagame all the contestants are aiming to win, rather than to maximize their score (except for the ones who are just aiming to troll the rest of us by submitting humorous bots). In that sense the situation is not really a true prisoner’s dilemma.