This is because I think that the counterexample given here dissolves if there is an additional path without node from the matchmaking policy to the priced payed
I think you are using some mental model where ‘paths with nodes’ vs. ‘paths without nodes’ produces a real-world difference in outcomes. This is the wrong model to use when analysing CIDs. A path in a diagram -->[node]--> can always be replaced by a single arrow --> to produce a model that makes equivalent predictions, and the opposite operation is also possible.
So the number of nodes on a path better read as a choice about levels of abstraction in the model, not as something that tells us anything about the real world. The comment I just posted with the alternative development of the game model may be useful for you here, it offers a more specific illustration of adding nodes.
I think you are using some mental model where ‘paths with nodes’ vs. ‘paths without nodes’ produces a real-world difference in outcomes. This is the wrong model to use when analysing CIDs. A path in a diagram -->[node]--> can always be replaced by a single arrow --> to produce a model that makes equivalent predictions, and the opposite operation is also possible.
So the number of nodes on a path better read as a choice about levels of abstraction in the model, not as something that tells us anything about the real world. The comment I just posted with the alternative development of the game model may be useful for you here, it offers a more specific illustration of adding nodes.