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On Rational Inattention with Arbitrary Choice Sets

Chris Engh

Abstract

This paper points out that rational inattention is a nested regularized optimal transport problem. We use entropic optimal transport to establish the main results in Matejka and McKay (2015) and Caplin, Dean, and Leahy (2019) and extend them to arbitrary choice sets.

On Rational Inattention with Arbitrary Choice Sets

Abstract

This paper points out that rational inattention is a nested regularized optimal transport problem. We use entropic optimal transport to establish the main results in Matejka and McKay (2015) and Caplin, Dean, and Leahy (2019) and extend them to arbitrary choice sets.
Paper Structure (11 sections, 23 theorems, 92 equations)

This paper contains 11 sections, 23 theorems, 92 equations.

Table of Contents

  1. Introduction
  2. The Schrödinger Bridge Problem
  3. Rational Inattention in Polish Spaces
  4. Some Basic Existence Results
  5. Optimal Information Policies
  6. Schrödinger Potentials
  7. Potentials Under Optimal Information Policies
  8. Statistical Mechanical Connections
  9. A Second Look at the Normalization Condition
  10. A Second Look at the Blahut-Arimoto Algorithm
  11. Conclusion

Key Result

Theorem 1

For each $\nu$, there exists a unique Schrödinger bridge $P\in \Pi(\nu,\mu)$ that attains the supremum in eq:SBP.

Theorems & Definitions (38)

  • Theorem 1
  • Theorem 2: Existence and uniqueness of potentials
  • Corollary 2.1: Additive separability
  • Theorem 3: Schrödinger Equations
  • Theorem 4: Duality
  • Lemma 5
  • proof
  • Theorem 6
  • proof
  • Definition 1
  • ...and 28 more