When I started this dive into acausal trade, I expected to find subtle and interesting theoretical considerations. Instead, most of the issues are practical.
The big two theoretical questions are whether we model infinite worlds with infinitely many agents, and whether we should agree to some ‘pre-existence’ deal with all agents, including those that don’t and cannot exist. We lay aside the infinite case for the time being; pre-existence deals simply lead to all agents maximising a single utility joint function. There are many issues with that - why would the agents accept a deal that gives them nothing at the moment they accept it, how can the agents share a common prior, how much effort are they required to make to not deal with logically impossible agents, and so on - but it’s a possible option.
Without prexistence deals, then the situation is not hard to model, and though practical issues seems to dominate acausal trade. There is the perennial issue of how to divide gains from trade and how to avoid extortion. There is a “Double decrease”: when an acausal trade network has fewer contributors, then those contributors also contribute less (since they derive lower advantage from doing so), compounding the decrease (and a converse result for larger trade networks).
There are many reasons an acausal trade network could be smaller. All agents could be unusual and distinct, making it almost impossible to figure out what agents actually exist. The different utilities could fail to be compatible in various ways. The agent’s decision algorithms and concepts of fairness could be incompatible. And many agents could be deliberately designed to not engage in acausal trade.
Against that all, the number \(N\) of potential agents could be so absurdly high that a lot of acausal trade happens anyway. This is probably necessary, to compensate for the extreme guesswork that goes into acausal trade: all the other agents exist only in our heads. Trade is still possible with such agents, but we shouldn’t forget our potential biases and errors when we attempt that estimation.
The only major detailed example I know of that illustrates acausal trade, is Scott’s example here. There an AI that realises it’s likely not the first AI, and attempts to surrender by simulating the reaction of a potential earlier AI.
Note that this is not acausal, it’s an acausal-like approach to estimate the reaction of other AIs during future causal interactions.
In any case, the AI ends up tapping into an acausal network of AIs with the joint agreement of non-interference for current and future AIs that might be brought into existence - a weaker version of the “universal utility” that exists for pre-existence deals.