Any prior work on mutiagent dynamics for continuous distributions over agents?

post by Quintin Pope (quintin-pope) · 2022-06-01T18:12:02.963Z · LW · GW · No comments

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Typical work on game theory, economics or multiagent negotiations assumes that there are a finite number of discrete agents. What if, instead, there's a continuous distribution over possible agents? Further, is there any work looking at the case where actions are taken by agents discretely sampled from that distribution? I.e., suppose we have a distribution over possible agents, then at each time step, we stochastically sample a single discrete agent from that distribution and allow it to act. Is there any work on the sorts of equilibria we might see?

Additionally, suppose the actions of the sampled agents can then influence the distribution over future agents. How does that change things? E.g.,  it seems clear enough that we should expect there to be attractors around agents whose actions cause more frequent sampling of agents similar to themselves, but are there other dynamics we should expect?

I ask this question because I'm interested in a multiagent perspective on the mind, but think that it's unlikely that the mind contains a discrete, finite set of subagents, and more likely that it contains (something like) a continuous distribution over possible agentic computations. 

Thanks for any help you can provide!

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