This post isn’t really correct about what distinguishes CDT from EDT or TDT. The distinction has nothing to do with the presence of other agents and can be seen in the absence of such (e.g. Smoking Lesion). Indeed neither decision theory contains a notion of “other agents”; both simply regard things that we might classify as “other agents” simply as features of the environment.
Fundamentally, the following paragraph is wrong:
X wants to maximize its expected utility. If there were no other agents, this would be simple: calculate the expected value of each action (given its information on how likely each consequence is to happen if it does this action or that), then perform the action that results in the highest expected value.
The difference between these theories is actually in how they interpret the idea of “how likely each consequence is to happen if it does this action or that”; hence they differ even in that “simple” case.
(Note: I’m only considering CDT, EDT, and TDT here. I think the others may work by some other mechanism?)
The difference between these theories is actually in how they interpret the idea of “how likely each consequence is to happen if it does this action or that”; hence they differ even in that “simple” case.
EDT does differ from CDT in that case (hence the Smoking Lesion problem), but EDT is clearly wrong to do so, and I can’t think of any one-player games that CDT gets wrong, or in which CDT disagrees with TDT.
both simply regard things that we might classify as “other agents” simply as features of the environment.
I don’t think this is right in general- I realized overnight that these decision theories are underspecified on how they treat other agents, so instead they should be regarded as classes of decision theories. There are some CDT agents who treat other agents as uncertain features of the environment, and some that treat them as pure unknowns that one has to find a Nash equilibrium for. Both satisfy the requirements of CDT, and they’ll come to different answers sometimes.
(That is, if X doesn’t have a very good ability to predict how Y works, then a “feature of the environment” CDT will treat Y’s action with an ignorance prior which may be very different from any Nash equilibrium for Y, and X’s decision might not be an equilibrium strategy. If X has the ability to predict Y well, and vice versa, then the two should be identical.)
This post isn’t really correct about what distinguishes CDT from EDT or TDT. The distinction has nothing to do with the presence of other agents and can be seen in the absence of such (e.g. Smoking Lesion). Indeed neither decision theory contains a notion of “other agents”; both simply regard things that we might classify as “other agents” simply as features of the environment.
Fundamentally, the following paragraph is wrong:
The difference between these theories is actually in how they interpret the idea of “how likely each consequence is to happen if it does this action or that”; hence they differ even in that “simple” case.
(Note: I’m only considering CDT, EDT, and TDT here. I think the others may work by some other mechanism?)
EDT does differ from CDT in that case (hence the Smoking Lesion problem), but EDT is clearly wrong to do so, and I can’t think of any one-player games that CDT gets wrong, or in which CDT disagrees with TDT.
I don’t think this is right in general- I realized overnight that these decision theories are underspecified on how they treat other agents, so instead they should be regarded as classes of decision theories. There are some CDT agents who treat other agents as uncertain features of the environment, and some that treat them as pure unknowns that one has to find a Nash equilibrium for. Both satisfy the requirements of CDT, and they’ll come to different answers sometimes.
(That is, if X doesn’t have a very good ability to predict how Y works, then a “feature of the environment” CDT will treat Y’s action with an ignorance prior which may be very different from any Nash equilibrium for Y, and X’s decision might not be an equilibrium strategy. If X has the ability to predict Y well, and vice versa, then the two should be identical.)