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Planet Haskell

A deep dive into computing Nash equilibrium strategies for Terminal Maneuvers, a two-player game simulating a missile evading a laser defense system. Starting from simple endgame scenarios and working backward, the analysis uses linear algebra to find mixed strategies for both players. When the strategy space grows (e.g., 4 fuel remaining), naive linear algebra yields negative probabilities, requiring linear programming to find valid minimax solutions. The key insight is that optimal play for both sides often means ignoring certain moves entirely — for example, neither player should involve burning/predicting 3 fuel when 4 fuel remains — because doing so would worsen their own expected outcome across subsequent rounds. Playing optimally, Missile has approximately a 32.3% chance of winning with 7 starting fuel, slightly higher than the empirical 25% estimate.

Nash Equilibrium for Terminal Maneuvers