If the hosts move first logically, then TDT will lead to the same outcomes as CDT, since it’s in each host’s interest to precommit to incentivising the human to pick their own box
It’s in the hosts interests to do that if they think the player is CDT, but it’s not in their interests to commit to doing that. They don’t lose anything by retaining the ability to select a better strategy later after reading the players mind.
Yes they do. For simplicity suppose there are only two hosts, and suppose host A precommits to not putting money host B’s box, while host B makes no precommitments about how much money he will put in host A’s box. Then the human’s optimal strategy is “pick host A’s box with probability 1 - x epsilon, where x is the amount of money in host A’s box”. This incentivizes host B to maximize the amount in host A’s box (resulting in payoff ~101 for the human), but it would have been better for him if he had precommitted to do the same as A, since then by symmetry his box would have been picked half the time instead of 101 epsilon of the time.
It’s in the hosts interests to do that if they think the player is CDT, but it’s not in their interests to commit to doing that. They don’t lose anything by retaining the ability to select a better strategy later after reading the players mind.
Yes they do. For simplicity suppose there are only two hosts, and suppose host A precommits to not putting money host B’s box, while host B makes no precommitments about how much money he will put in host A’s box. Then the human’s optimal strategy is “pick host A’s box with probability 1 - x epsilon, where x is the amount of money in host A’s box”. This incentivizes host B to maximize the amount in host A’s box (resulting in payoff ~101 for the human), but it would have been better for him if he had precommitted to do the same as A, since then by symmetry his box would have been picked half the time instead of 101 epsilon of the time.