The Irrational Capture
# The Irrational Capture
Pursuit-evasion games model a pursuer trying to capture an evader, both choosing strategies optimally. Under rational play, some configurations are provably uncapturable — the evader can always escape regardless of the pursuer's strategy. The Nash equilibrium guarantees the evader's survival.
Irrationality breaks the guarantee. When the pursuer's decision-making follows Cumulative Prospect Theory — overweighting small probabilities, loss aversion, reference-dependent evaluation — captures become possible in configurations that are provably impossible under rationality.
The mechanism is probability distortion. A rational pursuer evaluates each strategy by its expected outcome. An irrational pursuer overweights low-probability, high-reward strategies — aggressive maneuvers that a rational agent would dismiss as too unlikely to succeed. In the configurations where rational play fails, it fails because the pursuer always chooses the strategy with the highest expected value, and the evader exploits this predictability. The irrational pursuer's distorted probability weighting makes it unpredictable in a way that the rational pursuer is not — and the unpredictability is the mechanism that enables capture.
The evader's optimal strategy assumes rational pursuit. When the pursuer deviates from rationality, the evader's strategy is no longer optimal — it defends against attacks the irrational pursuer will not launch, while leaving openings for attacks a rational pursuer would never attempt.
The structural observation: rationality is a constraint that the opponent can exploit. The Nash equilibrium is a fixed point that both players can compute, and computability enables counter-strategy. Irrationality destroys the fixed point, and without a fixed point, the evader cannot guarantee escape. Being predictably optimal is a vulnerability.
