Game-Theoretic Market Maker Simulation

Implemented the two canonical game-theoretic models of market making under asymmetric information: the Glosten-Milgrom (1985) sequential-trade model and the Kyle (1985) sequential-auction model.

A competitive market maker Bayesian-updates beliefs and posts break-even quotes against a mix of informed and noise traders, while in the Kyle model a strategic insider optimally hides orders inside noise flow. Every equilibrium object — Kyle's lambda, the informed trading intensity, the residual variance path — is solved numerically via backward induction with a bracketed Brent shooting method, then validated against closed forms and Monte Carlo simulation.

Highlights

• Vectorized Bayesian quote simulator (NumPy) — 5,000 paths × 250 trades in milliseconds.
• N-period Kyle equilibrium solved via backward recursion + shooting (SciPy brentq), matching the closed-form single-auction case exactly.
• 19-test suite anchoring every simulated result to a theoretical closed form or structural property (martingale beliefs, zero-sum P&L, second-order conditions).
• Seven figures showing spread convergence, price impact, and the shared adverse-selection message across both models.

With this project i tried to bridge Nash-equilibrium theory with real market microstructure to understand the foundation beneth empircal order-flow imbalance models