So, I understand the argument that having more memory than your opponent is marginalized, and I then understand why, if you have a good memory-one strategy, you may as well just play oblivious (directly marginalizing the opponent's memory).
Appendix A: """The importance of this result is that the player with the
shortest memory in effect sets the rules of the game. A player with a good memory-one strategy can force the game to be played, effectively, as memory-one. She cannot be undone by another player’s longer-memory strategy."""
However, I'm having a hard time understanding how a memory-one strategy actually can be good, given that if your opponent has a theory of mind you apparently want to be paying enough attention to notice and dial down your extortion factor.
Discussion: """However, if she imputes to Y a theory of mind about herself, then she should remain engaged and watch for evidence of Y’s refusing the ultimatum (e.g., lack of evolution favorable to both)."""
How does one actually "remain engaged and watch for evidence" without having access to at least as much memory as their opponent's theory? It would seem that the "should" in this paragraph undermines the "can" in the previous one due to a conflict over "good".
What's happening here, I believe, is that neither of the players are actually playing a memory-one game. They extract a result for memory-one games and try to apply it to reason about a memory-N game, which I believe might be an error.
The "evolutionary" strategy used by Y is in fact a way for Y to base their decision on the outcome of many previous games. X is similarly using a long-term strategy. In the end, the players end up in a meta-game that is similar to the original one.
Note how this meta-game only works if both players agree to it -- if X is "out to lunch", as they put it, or if Y was simply playing a memory-one strategy without evolutionary adaption, the meta-game does not exist.
The title holds - they show how to use a local optimum to exploit a hill-climbing evolutionary player. However this can not be used to beat a true memory-one player, and I think the assumption that Y would require a "theory of mind" to counter this strategy is unfounded.
Appendix A: """The importance of this result is that the player with the shortest memory in effect sets the rules of the game. A player with a good memory-one strategy can force the game to be played, effectively, as memory-one. She cannot be undone by another player’s longer-memory strategy."""
However, I'm having a hard time understanding how a memory-one strategy actually can be good, given that if your opponent has a theory of mind you apparently want to be paying enough attention to notice and dial down your extortion factor.
Discussion: """However, if she imputes to Y a theory of mind about herself, then she should remain engaged and watch for evidence of Y’s refusing the ultimatum (e.g., lack of evolution favorable to both)."""
How does one actually "remain engaged and watch for evidence" without having access to at least as much memory as their opponent's theory? It would seem that the "should" in this paragraph undermines the "can" in the previous one due to a conflict over "good".