The definition may not be principled, but there’s something that feels a little bit right about it in context. There are various ways to “stay in the logical past” which seem similar in spirit to migueltorrescosta’s remark, like calculating your opponent’s exact behavior but refusing to look at certain aspects of it. The proposal, it seems, is to iterate already-iterated games by passing more limited information of some sort between the possibly-infinite sessions. (Both your and the opponent’s memory gets limited.) But if we admit that Miguel’s “iterated play without memory” is iterated play, well, memory could be imperfect in varied ways at every step, giving us a huge mess instead of well-defined games and sessions. But, that mess looks more like logical time at least.
Not having read the linked paper yet, the motivation for using iterated or meta-iterated play is basically to obtain a set of counterfactuals which will be relevant during real play. Depending on the game, it makes sense that this might be best accomplished by occasionally resetting the opponent’s memory.
I have been thinking a bit about evolutionarily stable equilibria, now. Two things seem interesting (perhaps only as analogies, not literal applications of the evolutionarily stable equilibria concept):
The motivation for evolutionary equilibria involves dumb selection, rather than rational reasoning. This cuts the tricky knots of recursion. It also makes the myopic learning, which only pays attention to how well things perform in of round, seem more reasonable. Perhaps there’s something to be said about rational learning algorithms needing to cut the knots of recursion somehow, such that the evolutionary equilibrium concept holds a lesson for more reflective agents.
The idea of evolutionary stability is interesting because it mixes the game and the metagame together a little bit: the players should do what is good for them, but the resulting solution should also be self-enforcing, which means consideration is given to how the solution shapes the future dynamics of learning. This seems like a necessary feature of a solution.
The definition may not be principled, but there’s something that feels a little bit right about it in context. There are various ways to “stay in the logical past” which seem similar in spirit to migueltorrescosta’s remark, like calculating your opponent’s exact behavior but refusing to look at certain aspects of it. The proposal, it seems, is to iterate already-iterated games by passing more limited information of some sort between the possibly-infinite sessions. (Both your and the opponent’s memory gets limited.) But if we admit that Miguel’s “iterated play without memory” is iterated play, well, memory could be imperfect in varied ways at every step, giving us a huge mess instead of well-defined games and sessions. But, that mess looks more like logical time at least.
Not having read the linked paper yet, the motivation for using iterated or meta-iterated play is basically to obtain a set of counterfactuals which will be relevant during real play. Depending on the game, it makes sense that this might be best accomplished by occasionally resetting the opponent’s memory.
I have been thinking a bit about evolutionarily stable equilibria, now. Two things seem interesting (perhaps only as analogies, not literal applications of the evolutionarily stable equilibria concept):
The motivation for evolutionary equilibria involves dumb selection, rather than rational reasoning. This cuts the tricky knots of recursion. It also makes the myopic learning, which only pays attention to how well things perform in of round, seem more reasonable. Perhaps there’s something to be said about rational learning algorithms needing to cut the knots of recursion somehow, such that the evolutionary equilibrium concept holds a lesson for more reflective agents.
The idea of evolutionary stability is interesting because it mixes the game and the metagame together a little bit: the players should do what is good for them, but the resulting solution should also be self-enforcing, which means consideration is given to how the solution shapes the future dynamics of learning. This seems like a necessary feature of a solution.