I don't think you've misunderstood; in fact I share your position.

Do you also reject compatibilist accounts of free will? I think the basic point at issue here is whether or not a fully determined action can be genuinely 'chosen', any more than the past events that determine it.

The set of assumptions that undermines CDT also ensures that the decision process is nothing more than the deterministic consequence (give or take some irrelevant randomness) of an earlier state of the world + physical law. The 'agent' is a fully determined cog in a causally closed system.

In the same-source-code-PD, at the beginning of the decision process each agent knows that the end result will either be mutual cooperation or mutual defection, and also that the following propositions must either be all true or all false:

1. 'I was programmed to cooperate'
2. 'the other agent was programmed to cooperate'
3. 'I will cooperate'
4. 'the end result will be mutual cooperation'

The agent wants Proposition 4 -- and therefore all of the other propositions -- to be true.

Since all of the propositions are known to share the same truth value, choosing to make Proposition 3 true is equivalent to choosing to make all four propositions true -- including the two that refer to past events (Propositions 1 and 2). So either the agent can choose the truth value of propositions about the past, or else Proposition 3 is not really under the agent's control.

I'd be interested to know whether those who disagree with me/us see a logical error above, or simply have a concept of choice/agency/free will/control that renders the previous paragraph either false or unproblematic (presumably because it allows you to single out Proposition 3 as uniquely under the agent's control, or it isn't so fussy about temporal order). If the latter, is this ultimately a semantic dispute? (I suspect that some will half-agree with that, but add that the incompatibilist notion of free will is at best empirically false and at worst incoherent. I think the charge of incoherence is false and the charge of empirical falsity is unproven, but I won't go into that now.)

In any case, responses would be appreciated. (And if you think I'm completely mistaken or confused, please bear in mind that I made a genuine attempt to explain my position clearly!)