A game-theoretic approach to incentivize landowners to mitigate an emerald ash borer outbreak

This article addresses the challenge posed by the Emerald Ash Borer (EAB), a wood-boring insect that threatens to kill ash trees, one of the North America's most vital tree genera. Current strategies include monitoring, treatment, and removal. However, the absence of a private-public partnership hinders progress on private ash trees. We propose two cost-sharing programs where local governments reimburse landowners for their management costs. This approach considers the EAB's dynamic growth over two periods based on different treatment decisions. Two mathematical models are developed for designing reimbursements: one based on the number of infested trees and another on the number of treated trees. We derive analytical solutions for the optimal treatment decisions and reimbursements in the first period. Our study reveals that treatment effectiveness and the likelihood of new infestations in the second period influence the optimal decisions. Comparing the reimbursement models, the treatment-based program proves more effective, encouraging landowners to treat more trees with higher reimbursements and overall benefits. Further, we show that continuing EAB treatment beyond the 2-year cost-sharing program is expected to yield superior long-term benefits. The approach seeks to foster private-public partnerships in addressing environmental challenges through resource sharing, such as managing water, land, and wildfires.