Continuation-Adjusted Full-Support Indifference in a Feedback Stackelberg Attacker--Defender Attrition Game

Abstract

Successful attacks that remove assets break two familiar static regularities: coverage need not deter attack, and the defender need not push coverage until its budget or an individual target saturates. We analyse a finite-horizon attacker--defender attrition game under a stagewise feedback-recommitment strong Stackelberg equilibrium. Our central result is a continuation adjustment that converts each state--period node into a static security game with shifted payoffs. At feasible full-support nodes, coverage remains indexed by one scalar attacker value, so backward induction uses scalar interval and endpoint calculations; boundary-support nodes require conditional linear programmes. Continuation losses can reverse an attacker's coverage swing, making a covered asset more attractive because it survives for later attacks. A three-asset, two-period instance is solved globally for every discount factor. It exhibits an exact singular threshold at which the optimal set expands, the selected policy jumps, and the defender abandons a previously protected asset and leaves budget unused with no target saturated, although both players' values remain continuous.

arXiv comment18 pages, one figure