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Information Design and Full Implementation in Nonatomic Games

Frederic Koessler, Marco Scarsini, Tristan Tomala

Abstract

This paper studies the implementation of Bayes correlated equilibria in symmetric Bayesian games with nonatomic players, using direct information structures and obedient strategies. The main results demonstrate full implementation in a class of games with negative payoff externalities, such as congestion and Cournot games. Specifically, if the game admits a strictly concave potential in every state, then for every Bayes correlated equilibrium outcome with finite support and rational action distributions, there exists a direct information structure that implements this outcome under all equilibria. When the potential is weakly concave, we show that all equilibria implement the same expected total payoff. Additionally, all Bayes correlated equilibria, including those with infinite support or irrational action distributions, are approximately implemented.

Information Design and Full Implementation in Nonatomic Games

Abstract

This paper studies the implementation of Bayes correlated equilibria in symmetric Bayesian games with nonatomic players, using direct information structures and obedient strategies. The main results demonstrate full implementation in a class of games with negative payoff externalities, such as congestion and Cournot games. Specifically, if the game admits a strictly concave potential in every state, then for every Bayes correlated equilibrium outcome with finite support and rational action distributions, there exists a direct information structure that implements this outcome under all equilibria. When the potential is weakly concave, we show that all equilibria implement the same expected total payoff. Additionally, all Bayes correlated equilibria, including those with infinite support or irrational action distributions, are approximately implemented.

Paper Structure

This paper contains 12 sections, 8 theorems, 75 equations.

Table of Contents

  1. Introduction
  2. Related Literature
  3. Organization of the Paper
  4. Notation
  5. The Model
  6. Examples
  7. Partial Implementation
  8. Potential Games and Full Implementation
  9. Potential Games
  10. Full Implementation
  11. Optimality of Deterministic BCWE
  12. List of Symbols and Acronyms

Key Result

Theorem 4.1

Let $\mu$ be a BCWE and $\psi \colon \mathcal{Y} \times \Theta \to \mathbb{R}$ be a continuous function. For all $\varepsilon>0$, there exists a direct information structure $\mathcal{I}$ such that the obedient interim flow profile $\breve\boldsymbol{y}_{\mathcal{I}}$ is a BWepsE of $(\Gamma,\mathca Further, if $\mu$ has finite support and if all flows in the support of $\mu$ are rational, then th

Theorems & Definitions (29)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4
  • Example 3.1: Platform access with network effects and congestion
  • Example 3.2: Entry on a market with uncertain production cost
  • Theorem 4.1
  • proof : Proof of \ref{['thm:partialBI']}
  • Definition 5.1
  • Lemma 5.2
  • ...and 19 more