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In contract theory and mechanism design, if the agents have one-dimensional characteristics, then they are usually considered as a contiuum on $\mathbb R$; if they have n-dimensional type, then they are in a contiuum on $\mathbb R^n$.

Naturally, if those (n-dimensional) types have some sort of correlations, then we could have a manifold of agents!

Or, if "n" is infinite, then we have agents on the infinite dimensional vector space.

Are there any research considered a manifold of agents?

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    $\begingroup$ Something like services.bepress.com/wilson/art20 ? $\endgroup$ Commented Oct 10, 2017 at 15:12
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    $\begingroup$ @MichaelGreinecker I was reading the same paper, too! This paper could be considered as "agents' types are on a infinite dimensional vector subspace $V$", and sometimes, a general topological manifold. $\endgroup$
    – High GPA
    Commented Oct 10, 2017 at 19:30

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