Mixed land ownership affects the scope for cooperative bargaining between jurisdictions to undertake control activities to slow the spread of an invasive species. We consider a problem in which emerald ash borer (EAB) spreads from an infested to an uninfested jurisdiction, where both contain ash trees on public and private land. We develop a dynamic model of cooperative Nash bargaining to examine how the mix of land ownership within each municipality affects the path of a negotiated transfer payment from the uninfested to the infested jurisdiction. Using a numerical simulation, we demonstrate that a bargaining agreement can be reached only below a threshold level of public land ownership in the infested municipality. The value of this threshold depends on the effectiveness of the transfer payment in supporting more intensive control efforts, such as tree removal, that delay spread. In a landscape with mixed ownership, free riding by private landowners on the public control effort is one factor that leads to a decrease in this threshold. We also find that in the presence of free riding, a bargaining agreement can only exist if the jurisdictions commit to a path of transfer payments that spans multiple years. This suggests a role for higher government to play in supporting multi-year cross-jurisdictional agreements.