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Proof of Concept / Game-Theoretic Multi-Agent RL

Competitive Response
Simulator

Nash Equilibrium Discovery in 1L NSCLC via Multi-Agent Q-Learning

Two competing oncology brand teams simultaneously learn optimal commercial strategies via independent Q-learning. The engine simulates head-to-head competition across 9 strategy combinations — pricing tier, messaging approach, and channel investment — and discovers Nash equilibria where neither brand can improve by unilaterally changing strategy. Built entirely in-browser with no backend dependencies.

Multi-Agent RLQ-LearningNash EquilibriumGame TheoryPayoff MatrixCompetitive Strategy

Disclaimer: This is a proof-of-concept using synthetic competitive dynamics. All brand names, market share figures, and strategy payoffs are illustrative. This tool does NOT represent actual competitive intelligence or commercial strategies of any pharmaceutical company. Not intended for actual business decisions.

Simulating competitive dynamics...

Training 300 episodes × 24 months × 2 agents

Technical Architecture

Independent Q-Learning

Each brand maintains its own Q-table mapping (own_share_bucket × opponent_last_action) → strategy value. Brands update simultaneously using Bellman equations — treating the opponent as part of the environment. ε-greedy exploration decays over 300 training episodes.

Payoff Matrix Construction

Each of the 81 strategy pair combinations is simulated for 100 rounds to estimate expected market share changes for both brands. The resulting 9×9 payoff matrix encodes how each strategy performs against every competitor response — the foundation for Nash equilibrium analysis.

Nash Equilibrium Detection

Pure-strategy Nash equilibria found by checking: can either brand improve by deviating? A strategy pair (a*, b*) is Nash if payoffA(a*, b*) ≥ payoffA(a, b*) for all a, and similarly for brand B. Nash proximity scores quantify near-equilibrium states.

References

  • Nash JF. Equilibrium points in n-person games. Proc Natl Acad Sci. 1950;36(1):48-49.
  • Watkins CJ, Dayan P. Q-learning. Machine Learning. 1992;8(3-4):279-292.
  • Shoham Y, Powers R, Grenager T. Multi-agent reinforcement learning: a critical survey. Technical Report, Stanford. 2003.
  • Fudenberg D, Tirole J. Game Theory. MIT Press; 1991. Chapter 1: Normal-Form Games and Nash Equilibrium.
  • Smit E, et al. Competitive dynamics in pharmaceutical markets. J Health Econ. 2017;54:134-149.

Daniel Tran, PharmD

UC San Diego — Skaggs School of Pharmacy

Source code MIT. Content © 2026 Daniel Tran (CC BY-NC-SA 4.0).