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Improving Cooperation in Language Games with Bayesian Inference and the Cognitive Hierarchy
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Builds Bayesian Codenames spymaster and guesser agents that maintain beliefs over teammate models (word embeddings and cognitive-hierarchy levels) with Gaussian embedding noise, and shows better win rates when semantics is uncertain.
Problem
Cooperative language games require agents to coordinate despite differing semantics (word embeddings) and pragmatics (strategies), and static agents perform poorly when their assumptions about a teammate are wrong.
Approach
Combine a prior over partner types (multiple word embeddings and deductive-hierarchy levels) with Gaussian noise on embeddings, update beliefs via Bayes' rule from observed teammate actions, and choose clues or guesses that maximize expected value under a heuristic utility.
Key results
- Uncertain Bayesian spymaster (noise 1.0) averages 0.872 win rate with out-of-distribution guessers in deterministic environment vs 0.718 for best single model.
- In stochastic environments, the noisy Bayesian spymaster averages 0.625 with out-of-distribution guessers vs 0.468 for the best model.
- Bayesian guessers rarely matched the best single model; DG_B averaged 0.975 with in-distribution spymasters in deterministic environment versus 0.926 for best model.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add assumed embedding noise to the Bayesian spymaster (ablation) | SM_B · Codenames, deterministic environment, in-distribution guessers | win rate: 0.960 -> 0.860 | Hurt |
| Add assumed embedding noise to the Bayesian spymaster (ablation) | SM_B · Codenames, deterministic environment, out-of-distribution guessers | win rate: 0.761 -> 0.872 | Helped |
| Add assumed embedding noise to the Bayesian spymaster (ablation) | SM_B · Codenames, stochastic environment, in-distribution guessers | win rate: 0.370 -> 0.450 | Helped |
| Add assumed embedding noise to the Bayesian spymaster (ablation) | SM_B · Codenames, stochastic environment, out-of-distribution guessers | win rate: 0.477 -> 0.625 | Helped |
| Use a Bayesian spymaster instead of the best static spymaster | Codenames · Deterministic environment, in-distribution guessers | win rate: 0.926 -> 0.960 | Helped |
| Use a Bayesian spymaster instead of the best static spymaster | Codenames · Deterministic environment, out-of-distribution guessers | win rate: 0.718 -> 0.872 | Helped |
| Use a Bayesian spymaster instead of the best static spymaster | Codenames · Stochastic environment, in-distribution guessers | win rate: 0.370 -> 0.450 | Helped |
| Use a Bayesian spymaster instead of the best static spymaster | Codenames · Stochastic environment, out-of-distribution guessers | win rate: 0.468 -> 0.625 | Helped |
| Add assumed embedding noise to DG_B (ablation) | Bayesian guesser · Codenames, deterministic environment, in-distribution spymasters | win rate: 0.975 -> 0.962 | Hurt |
| Add assumed embedding noise to DG_B (ablation) | Bayesian guesser · Codenames, deterministic environment, out-of-distribution spymasters | win rate: 0.534 -> 0.522 | Hurt |
| Add assumed embedding noise to DG_B (ablation) | Bayesian guesser · Codenames, stochastic environment, in-distribution spymasters | win rate: 0.670 -> 0.733 | Helped |
| Add assumed embedding noise to DG_B (ablation) | Bayesian guesser · Codenames, stochastic environment, out-of-distribution spymasters | win rate: 0.423 -> 0.425 | No clear effect |
Surprising findings
- Bayesian spymasters outperform any of their constituent static models, even in the deterministic environment with the matching guesser embedding (d2v).
- Bayesian guessers almost never matched the best single model, attributed to the weaker signal a guesser receives about the spymaster.
Limitations
- Only first level of the cognitive hierarchy (k=1) was evaluated due to implementation difficulties.
- All experiments use simulated word-embedding agents; no human subjects.
- Bayesian guessers underperform the best single model.
Experimental setup
Benchmarks: simulated solitaire Codenames games
Metrics: win rate
Baselines: static level-0 spymaster per word embedding static level-0 guesser per word embedding best single model
Builds on: deductive hierarchy (level-k reasoning) cognitive hierarchy (Stahl) Rational Speech Act framework
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