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Acausal trade

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In acausal trade, two agents each benefit by predicting what the other wants and doing it, even though they might have no way of communicating or affecting each other, nor even any direct evidence that the other exists.

Background: Super-rationality and the one-shot Prisoner's Dilemma

This concept emerged out of the much-debated question of how to achieve cooperation on a one-shot Prisoner's Dilemma, where, by design, the two players are not allowed to communicate. On the one hand, a player who is considering the causal consequences of a decision ("Causal Decision Theory") finds that defection always produces a better result. On the other hand, if the other player symmetrically reasons this way, the result is an equilibrium of Defect/Defect, which is bad for both agents. If they could somehow converge on Cooperate, they would each do better, on their own utility measures. Given that the goal in decision theory is to maximize utility, the question is what decision theory would allow this beneficial equilibrium.

Douglas Hofstadter (see references) coined the term "super-rationality" to express this state of convergence. He illustrated it with a game in which twenty players, who do not know each other's identities, each get an offer. If exactly one player asks for the prize of a billion dollars, they get it, but if none or multiple players ask, no one gets it. Players cannot communicate, but each might reason that the others are reasoning similarly. The "correct" decision--the decision which maximizes expected utility for each player, *if* players symmetrically make the same decision--is to randomize a one-in-20 chance of asking for the prize.

Gary Drescher (see references) developed the concept further, introducing an ethical system called "acausal subjunctive morality." Drescher's approach relies on the agents being identical or at least similar, so that each agent can reasonably guess what the other will do based on facts about its own behavior, or even its own "source code." If it cooperates, it can use this correlation to infer that the other will probably also cooperate.

Acausal trade goes one step beyond this. The agents do not need to be identical, nor similar, nor have the same utility function. Moreover, they do not need to know what the other agents are like, nor even if they exist. In acausal trade, an agent may have to surmise the probability other agents, with utility function and proclivities, exists.


We have two agents, separated so that no interaction is possible. The separation can be simply because each is not aware of the location of the other; or else each may be prevented for some reason from communicating with or affecting the other. In an asymmetrical example, one agent may be in the other's future.

Other less prosaic scenarios can be used to illustrate cases where interaction is absolutely impossible. For example, the agents may be outside each other's light cones, or in separate parts of an Everett multiverse. But we can also talk of counterfactual "impossible possible worlds" as abstractions, as a model for probability distributions.

In acausal trade, the agents cannot count on reputation, retaliation, or outside enforcement to ensure cooperation. The agents cooperate because each knows that the other can somehow predict its behavior very well. (Compare Omega in Newcomb's problem.) Each knows that if it defects (respectively: cooperates), the other will (probabilistically) know this, and defect (respectively: cooperate).

Acausal trade can also be described in terms of (pre)commitment: Both agents commit to cooperate, and each has reason to think that the other is also committing.

Prediction mechanisms

For acausal trade to occur, each agent must infer that there is some probability that the other exists, and that the other will trade with it.

For the belief that the trading partner exists, we may have the simple case in which the agents are told this exogenously, as part of the scenario. But more interesting is the case in which the agent surmises the probability that the other exists.

A superintelligence might conclude that other superintelligences would tend to exist because increased intelligence is an convergent instrumenta goal for agents. Given the existence of a superintelligence, acausal trade is one of the tricks it would tend to use.

To take a more prosaic example, a person might realize that humans tend to be alike: Even without knowing about specific trading partners, they know there there exist other people with similar situations, goals, desires, challenges, resource constraints, and mental architectures.

Once an agent realizes that other agents might exist, there are different ways of describing how it can predict another agent's behavior, and specifically that the other agent can be an acausal trading partner.

  1. They might know each other's mental architectures (source code).
  2. In particular, they might know that they have identical or similar mental architecture, so that each one knows that its own mental processes approximately simulate the other's.
  3. They might be able to simulate each other (perhaps probabalistically), or to predict the other's behavior analytically. (Even we humans simulate each other's thoughts to guess what the other would do.)
  4. More broadly, it is enough to know (probabilistically) that the other is a powerful optimizer, that it has a certain utility function, and that it gets different utility from different resources. Seen mathematically, this is just an optimization problem: What is the best possible algorithm for an agent's utility function? If one agent could achieve optimal utility by "defecting," then, symmetrically, so could the other, resulting in Defect/Defect which generates inferior utility.

Decision Theories

Acausal trade is a special case of Updateless decision theory (or a variant like Functional Decision Theory). Unlike better-known forms of Decision theory, such as Causal decision theory, acausal trade and UDT take into account the agent's own algorithm as cause and caused.

In Causal Decision Theory, the agent's algorithm (implementation) is treated as uncaused by the rest of the universe, so that though the agent's decision and subsequent action can make a difference, its internal make-up cannot (except through that decision). In contrast, in UDT, the agents' own algorithms are treated as causal nodes, influenced by other factors, such as the logical requirement of optimality in a utility-function maximizer. In UDT, as in acausal trade, the agent cannot escape the fact that its decision to defect or cooperate constitutes strong Bayesian evidence as to what the other agent will do, and so it is better off cooperating.

Limitations and Objections

Acausal trade only works if the agents are smart enough to predict each other's behavior, and then smart enough to acausally trade. If one agent is stupid enough to "defect," and the second is smart enough to predict the first, then neither will cooperate.

Also, as in regular trade, acausal trade only works if the weaker side can offer resources that make it worth the stronger side's transaction costs.

A common objection to this idea: Why shouldn't the agent "cheat" and choose to defect? Can't it "at the last moment" back out after the other agent has committed? However, this approach takes into account only the direct effect of the decision, while in fact a sufficiently intelligent trading partner could predict the agent's choice, including that one, rendering the "cheating" approach suboptimal.

Another objection: Can an agent care about (have a utility function that takes into account) entities with which it can never interact, and about whose existence it is not certain? However, this is quite common even for humans today. We care about the suffering of other people in faraway lands about whom we know next to nothing. And in an even more clear-cut example of acausality, we are disturbed by the suffering of long-gone historical people, and wish that, counterfactually, the suffering had not happened. We even care about entities that we are not sure exist. For example: We might read some news report that a valuable archaeological find was destroyed in a distant country, yet at the same time read other news reports stating that the story is a fabrication. People even get emotionally attached to the fate of a fictional character.

An example of acausal trade with simple resource requirements

At its most abstract, the agents are simply optimization algorithms. As a toy example, let T be a utility function for which time is most valuable as a resource; while for utility function S, space is most valuable, and assume that these are the only two resources.

We will now choose the best algorithms for optimizing T. To avoid anthropomorphizing and asking what the agents will decide to do, we simply ask which algorithm--which source code--would give the highest expected utility for a given utility function. Thus, the choice of source code is "timeless": We treat it as an optimization problem across all possible strings of LISP. We assume that computing power is unlimited--mathematically, we are asking about argmax T.

We specify that there is a probability that either agent will be run in an environment where time is in abundance, and if not, some probability that it will be run in a space-rich universe.

If the algorithm for T is instantiated in a space-rich environment, it will only be able to gain a small amount of utility for itself, but S would be able to gain a lot of utility; and vice versa.

The question is what algorithm for T provides the most optimization power, the highest expected value of utility function T.

If it turns out that the environment is space-rich, the agent for T may run the agent (the algorithm) for S, increasing the utility for S, and symmetrically the reverse. This will happen if each concludes, that the optimum occurs when the other agent has the "trading" feature. Given that this is the optimal case, the acausal trade will occur.

Acausal trade with complex resource requirements

In the toy example above, resource requirements are very simple. In general, given that agents can have complex and arbitrary goals requiring a complex mix of resources, an agent might not be able to conclude that a specific trading partner has a meaningful change of existing and trading.

However, an agent can analyze the distribution of probabilities for the existence of other agents, and weight its actions accordingly. It will do acausal "favors" for one or more trading partners, weighting its effort according to its subjective probability that the trading partner exists. The expectation on utility given and received will come into a good enough balance to benefit the traders, in the limiting case of increasing super-intelligence.

Ordinary trade

Even ordinary trade can be analyzed acausally, using a perspective similar to that of Updateless decision theory. We ask: Which algorithm should an agent have to get the best expected value, summing across all possible environments weighted by their probability? The possible environments include those in which threats and promises have been made.

See also