The example you’ve given me shows that agents which implement exactly the same (high-level) algorithm can cooperate with each other. The metric I’m looking for is: how can we decide how similar two agents are when their algorithms are non-identical? Presumably we want a smoothness property for that metric such that if our algorithms are very similar (e.g. only differ with respect to some radically unlikely edge case) the reduction in cooperation is negligible. But it doesn’t seem like anyone knows how to do this.
One way I imagine dealing with this is that there is an oracle that tells us with certainty, for two algorithms and their decision situations, what the counterfactual possible joint outputs are. The smoothness then comes from our uncertainty about (i) the other agents’ algorithms (ii) their decision situation (iii) potentially the outputs of the oracle. The correlations vary smoothly as we vary our probability distributions over these things, but for a fully specified algorithm, situation, etc., the algorithms are always either logically identical or not.
Unfortunately, I don’t know what the oracle would be doing in general. I could also imagine that, when formulated this way, the conclusion is that humans never correlate with anything, for instance.
The example you’ve given me shows that agents which implement exactly the same (high-level) algorithm can cooperate with each other. The metric I’m looking for is: how can we decide how similar two agents are when their algorithms are non-identical? Presumably we want a smoothness property for that metric such that if our algorithms are very similar (e.g. only differ with respect to some radically unlikely edge case) the reduction in cooperation is negligible. But it doesn’t seem like anyone knows how to do this.
One way I imagine dealing with this is that there is an oracle that tells us with certainty, for two algorithms and their decision situations, what the counterfactual possible joint outputs are. The smoothness then comes from our uncertainty about (i) the other agents’ algorithms (ii) their decision situation (iii) potentially the outputs of the oracle. The correlations vary smoothly as we vary our probability distributions over these things, but for a fully specified algorithm, situation, etc., the algorithms are always either logically identical or not.
Unfortunately, I don’t know what the oracle would be doing in general. I could also imagine that, when formulated this way, the conclusion is that humans never correlate with anything, for instance.