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Informational Puts

Andrew Koh, Sivakorn Sanguanmoo, Kei Uzui

Abstract

We analyze how dynamic information should be provided to uniquely implement the largest equilibrium in binary-action coordination games. The designer offers an informational put: she stays silent if players choose her preferred action, but injects asymmetric and inconclusive public information if they lose faith. There is (i) no multiplicity gap: the largest (partially) implementable equilibrium can be implemented uniquely; and (ii) no commitment gap: the policy is sequentially optimal. Our results have sharp implications for the design of policy in coordination environments.

Informational Puts

Abstract

We analyze how dynamic information should be provided to uniquely implement the largest equilibrium in binary-action coordination games. The designer offers an informational put: she stays silent if players choose her preferred action, but injects asymmetric and inconclusive public information if they lose faith. There is (i) no multiplicity gap: the largest (partially) implementable equilibrium can be implemented uniquely; and (ii) no commitment gap: the policy is sequentially optimal. Our results have sharp implications for the design of policy in coordination environments.

Paper Structure

This paper contains 48 sections, 14 theorems, 191 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Related Literature
  3. Model
  4. Environment
  5. Payoffs
  6. Dynamic information policies
  7. Strategies and Equilibria
  8. Designer's problem under adversarial equilibrium selection
  9. Sequential Optimality
  10. Optimal dynamic information
  11. I. Belief and aggregate action near the upper dominance region.
  12. II. Belief and aggregate action far from upper dominance region.
  13. III. Designer-preferred action strictly dominated.
  14. IV. Sequential optimality.
  15. Construction of informational puts.
  16. ...and 33 more sections

Key Result

Theorem 1

In the limit $\eta \downarrow 0$, informational puts close the multiplicity gap and is sequentially optimal:

Figures (11)

  • Figure 1: Relationship between beliefs, equilibria, and action paths
  • Figure 2: Policy near upper dominance region
  • Figure 3: Chaining off-path information
  • Figure 4: Escaping the lower dominance region
  • Figure 5: Sequential optimality
  • ...and 6 more figures

Theorems & Definitions (40)

  • Definition 1: Lower dominance region
  • Definition 2
  • Definition 3: Tolerance, upward/downward jump sizes, belief direction
  • Definition 4: Maximal escape probability and beliefs
  • Theorem 1
  • proof
  • proof : Proof of Theorem \ref{['thrm:main']}
  • Definition 5
  • Lemma 1
  • proof : Proof of Lemma \ref{['lem: lipschitz']}
  • ...and 30 more