Adversarial procurement in two-value space: insights and evidence for conservation siting

The benefit-cost ratio is the canonical rule for filling a budget from a passive menu in the conventional planner’s optimisation problem. We show it can fail in a version of the problem we call adversarial procurement in two-value space, in which a mission-driven buyer acquires assets sequentially from a shared, shrinking pool against an active rival whose valuation also sets the buyer’s price. Cost then changes meaning: contested high-value assets are deferred while the rival removes them, and the ratio rule is dominated by a simpler value-first priority rule that ignores cost entirely, a pattern we call the knapsack reversal. Formal results prove the mechanism is structural. In a pure-rivalry model without budgets, a finite-board, distribution-free theorem shows value-first weakly dominates the ratio rule pathwise against a max-value rival; adding prices and budgets preserves the dominance asymptotically. A follower theorem extends the result to a subgame-perfect best-responding rival; diagnostic computations validate the reduction and stress-test the boundary cases. The strongest simple rule is interior and value-led, and how far it tilts toward pre-emption depends on whether the rival’s valuation is also a price. A priority tilt to the opposite end of the continuum, threat-targeting, is the standard instrument for raising additionality, and under adversarial rivalry produces a second reversal. Ranking by the rival’s coordinate alone sacrifices selection quality and is dominated by an alternative rule that admits value even when the rival cannot re-target (i.e. under zero leakage, the case in which it is conventionally optimal). Paradoxically, constraining leakage can raise welfare losses. Again, the robust response is to lead with the focal agent’s own value. Conservation siting provides the most empirically transparent instance of this structure, and both reversals bite: static cost-effectiveness priority rules are common and additionality has become a binding evaluation criterion. A Bolivia case study with 390 planning units demonstrates both reversals on a real, correlated, heavy-tailed landscape: static cost-effectiveness overstates realised conservation by 15–20%, a “disappointment gap” generated by the rival’s removal of the contested, high-value frontier.