Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isomorphism Properties of Optimality and Equilibrium Solutions under
  Equivalent Information Structure Transformations I: Stochastic Dynamic Teams   In stochastic optimal control, change of measure arguments have been crucial
for stochastic analysis. Such an approach is often called static reduction in
dynamic team theory (or decentralized stochastic control) and has been an
effective method for establishing existence and approximation results for
optimal policies. In this paper, we place such static reductions into three
categories: (i) those that are policy-independent (as those introduced by
Witsenhausen), (ii) those that are policy-dependent (as those introduced by Ho
and Chu for partially nested dynamic teams), and (iii) those that we will refer
to as static measurements with control-sharing reduction (where the
measurements are static although control actions are shared according to the
partially nested information structure). For the first type, we show that there
is a bijection between person-by-person optimal (globally optimal) policies of
dynamic teams and their policy-independent static reductions. For the second
type, although there is a bijection between globally optimal policies of
dynamic teams with partially nested information structures and their static
reductions, in general there is no bijection between person-by-person optimal
policies of dynamic teams and their policy-dependent static reductions. We also
establish a stronger negative result concerning stationary solutions. We
present sufficient conditions under which bijection relationships hold. Under
static measurements with control-sharing reduction, connections between
optimality concepts can be established under relaxed conditions. An implication
is a convexity characterization of dynamic team problems under static
measurements with control-sharing reduction. Finally, we introduce multi-stage
refinements of such reductions. Part II of the paper addresses similar issues
in the context of stochastic dynamic games, where further subtleties arise.

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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph