You should check out “Why Subagents?”. That post starts with the usual argument that acyclic preferences imply existence of a utility function, then shows that if we relax some of the assumptions, we actually get committees of utility-maximizers. Markets are my go-to example: they satisfy exactly the same “inexploitability” notions used by utility-existence proofs, but a market doesn’t have a utility function in general, because it has internal degrees of freedom which result in path-dependent aggregate preferences.
You should check out “Why Subagents?”. That post starts with the usual argument that acyclic preferences imply existence of a utility function, then shows that if we relax some of the assumptions, we actually get committees of utility-maximizers. Markets are my go-to example: they satisfy exactly the same “inexploitability” notions used by utility-existence proofs, but a market doesn’t have a utility function in general, because it has internal degrees of freedom which result in path-dependent aggregate preferences.