Minimax and Statistical Decisions in the Tactical Arrival Problem

Abstract: An aircraft flies an arrival into an airfield in a hostile environment. The aircraft may vary its approach path several ways: altitude, sector of flight, path over the ground, direction of turns, or runway used for landing, etc. In many situations, there is an enemy positioned near the airfield poised to fire a weapon at arriving aircraft. The position of the enemy is unknown to the pilot of the aircraft. Likewise, the flight path of the aircraft is unknown to the enemy. In this tactics problem, the pilot must decide the best way to vary his approach to avoid being shot.

We may describe the situation above in simple terms, as in the matching pennies game, or with exhaustive models requiring complex simulations to analyze. This paper presents a development and analysis of a minimax, game theoretic model (rational pilot vs. rational shooter) of the tactics problem and then related variants, particularly the tactics problem as a game of Nature vs. the rational pilot, where Nature is the fixed, but unknown, probability that a shooter is present in a quadrant, or alternately, where Nature is the overall distribution of the enemy. The TacticsArrival Problem, or TAP example, is the focal point, and this context will serve as the environment in which to develop general tools of decision theory, specific results needed to address the particularities of the tactics problem, and finally, validation of the model through data analysis and simulation.

Finally, we highlight incidences of Allais paradox, contradictions to the theory of decisions under uncertainty, in the tactical problem and propose a method for addressing these.