Yet CDT would have you evaluate an action by considering what happens if you replace the node Give? with a function that always returns that action. But this intervention does not affect the opponent, which reasons the same way!
This doesn’t seem obvious to me. It looks to me like the graph is faulty; there should be “TheirDecision” and “YourDecision” nodes, each successors of the Give? node, such that changing the Give? node causally affects both. The Give? node is a function; the decision nodes are its outputs. With the graph structured like that, you get sane behavior.
The notion of how to correctly construct that causal graph is, in itself, part of the decision theory. CDT constructs a faulty graph because CDT itself explicitly states that you control the “YourDecision” nodes, and that those nodes should be treated as having no predecessors.
This doesn’t seem obvious to me. It looks to me like the graph is faulty; there should be “TheirDecision” and “YourDecision” nodes, each successors of the Give? node, such that changing the Give? node causally affects both. The Give? node is a function; the decision nodes are its outputs. With the graph structured like that, you get sane behavior.
The notion of how to correctly construct that causal graph is, in itself, part of the decision theory. CDT constructs a faulty graph because CDT itself explicitly states that you control the “YourDecision” nodes, and that those nodes should be treated as having no predecessors.