Yes, they would appear to contradict each other. What's happening here, I believe, is that neither of the players are actually playing a memory-one game. They

Yes, they would appear to contradict each other. 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.