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Multi-Sender Persuasion: A Computational Perspective
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Studies multi-sender Bayesian persuasion with simultaneous independent senders, proves best-response NP-hardness and equilibrium PPAD-hardness, and proposes a discontinuous piecewise non-linear hypernetwork (DNL) with extra-gradient to find epsilon-local Nash equilibria that Pareto-dominate full-revelation and ReLU/DeLU-based solutions.
Problem
Computing best responses and Nash equilibria among multiple senders with informational advantage who simultaneously design signaling policies to persuade a single Bayesian receiver; the sender utilities are discontinuous and piecewise non-linear in policies.
Approach
A hypernetwork-based architecture that conditions higher-layer weights on the lower-layer ReLU activation pattern, making the approximated utility piecewise non-linear and discontinuous, so that extra-gradient can find epsilon-local Nash equilibria of multi-sender persuasion games.
Key results
- On real-world-style scenarios, the DNL network reports social welfare of 0.699 vs 0.599 (DeLU) and 0.498 (ReLU) in advertising of quality, and 4.344 vs 3.783 and 3.216 in Uber/Lyft.
- Epsilon-local equilibria found by extra-gradient on DNL networks Pareto-dominate those from ReLU and DeLU networks and full-revelation equilibria in synthetic experiments with 2 senders.
- Theory: computing a sender's best response is NP-hard even with n=2 senders and additive error 1/|Omega|^6; finding a Nash equilibrium is PPAD-hard in general.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use DNL instead of DeLU | ε-local equilibrium search · Advertising of Quality (Scenario 1) | social welfare: 0.599±0.003 -> 0.699±0.003 | Helped |
| use DNL instead of DeLU | ε-local equilibrium search · Advertising of Multiple Products (Scenario 2) | social welfare: 0.467±0.179 -> 0.526±0.004 | Helped |
| use DNL instead of DeLU | ε-local equilibrium search · Uber or Lyft (Scenario 3) | social welfare: 3.783±0.894 -> 4.344±0.885 | Helped |
Surprising findings
- The fixed full-revelation equilibrium can be Pareto-dominated by local equilibria, so revealing maximal information is not ideal for senders.
Limitations
- Only local (epsilon-) equilibria are found; global equilibrium computation is intractable per the hardness results.
- Equilibrium verification is done by random sampling of deviations rather than exact checking.
- Equilibrium verification complexity (co-NP hardness) is conjectured but not proven.
Experimental setup
Datasets: synthetic multi-sender persuasion games (Gaussian-sampled utilities) advertising and ride-hailing (Uber/Lyft) scenarios generated by the authors
Benchmarks: synthetic multi-sender persuasion benchmark (1,250 instances) advertising of quality advertising of multiple products Uber or Lyft
Metrics: approximation error sender ex-ante utility at epsilon-local NE social welfare
Baselines: ReLU network DeLU full-revelation equilibrium
Builds on: Bayesian Persuasion DeLU extra-gradient ReLU networks
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