Hm. So I think I reinvented the wheel to moderate success, then. In the blind, no-communication case, you play the bargaining equilibrium. With communication via source code, though, I didn’t make my wheel—following the bargaining equilibrium among strategies—very round. This is because you can use your source codes to send two random numbers, which lets you cooperate with the other player. But there are many different possible ways of doing this, each corresponding to a different equilibrium.
To have any chance of cooperating, and thus beating my slightly non-round wheel, you need a prior over opponents to let you narrow down the search for cooperation schemes (probably “pick the simplest”), and you need to randomize over the multiple remaining equilibria. And no cliqueishness here, since we’re trying to play blind.
Hm. So I think I reinvented the wheel to moderate success, then. In the blind, no-communication case, you play the bargaining equilibrium. With communication via source code, though, I didn’t make my wheel—following the bargaining equilibrium among strategies—very round. This is because you can use your source codes to send two random numbers, which lets you cooperate with the other player. But there are many different possible ways of doing this, each corresponding to a different equilibrium.
To have any chance of cooperating, and thus beating my slightly non-round wheel, you need a prior over opponents to let you narrow down the search for cooperation schemes (probably “pick the simplest”), and you need to randomize over the multiple remaining equilibria. And no cliqueishness here, since we’re trying to play blind.