But you really aren’t assuming that, you’re doing something much stranger.
Either the actual opponent is a rock, in which case it gains nothing from “winning” the game, and there’s no such thing as being more or less rational than something without preferences, or the actual opponent is the agent who wrote the number on the rock and put it in front of the agent, in which case the example fails because the game actually started with an agent explicitly trying to manipulate the LDT agent into underperforming.
But you really aren’t assuming that, you’re doing something much stranger.
Either the actual opponent is a rock, in which case it gains nothing from “winning” the game, and there’s no such thing as being more or less rational than something without preferences, or the actual opponent is the agent who wrote the number on the rock and put it in front of the agent, in which case the example fails because the game actually started with an agent explicitly trying to manipulate the LDT agent into underperforming.