As a bioinvasion spreads across a landscape from its point of introduction, damages rise roughly with the square of the distance from the original invasion. It is thus generally beneficial, at the landscape scale, to apply eradication or containment controls early if not immediately upon discovery. However, an individual property owner only has incentives to consider the costs and benefits of control on his/her own property rather than potential landscape-scale damages. Bioinvasions will therefore generally be under-controlled in a landscape of independent owners operating under a laissez-faire system. A mechanism is thus needed to induce early cooperative contributions to control costs from beneficiaries who would, without them, be invaded later. We develop a spatially-explicit, integrated model of invasion spread and human behavior to examine how different degrees of spatial cooperation affect patterns of invasion spread and the total costs and damages imposed. We compare individual laissez-faire, cooperative control by adjacent neighbors, and cooperative control by groups including more distant but nearby neighbors. As expected, private laissez-faire control decisions tend to under-control the invasion relative to socially optimal control under most circumstances. But a reasonably high fraction of first best payoffs can be achieved with only a modest geographical reach of cooperation. We also find that less extensive cooperation is needed to control invasions whose costs and damages otherwise lead to the largest externalities (circumstances with costs that are relatively low compared with damages). This suggests that even small amounts of cooperation to control bioinvasions can provide large social benefits.