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Cooperative Management of Invasive Species: A Dynamic Nash Bargaining Approach

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Abstract

We use a Nash bargaining framework to examine scope for bargaining in invasive species problems where spread depends on the employment of costly controls. Municipalities bargain over a transfer payment that slows spread but requires an infested municipality to forgo nonmarket benefits from the host species. We find that when the uninfested municipality has a relative bargaining power advantage, bargaining may attain the first-best solution. However, in many cases a short-term bargaining agreement is unlikely to succeed, which suggests a role for higher levels of government to facilitate long-term agreements even when the details are left to municipalities to negotiate.

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Notes

  1. Alternatively, this problem could be framed as one in which two coalitions bargain to prevent spread of an invasive species between their members to reflect a multilateral or multiple municipality problem.

  2. Nash proved that under certain conditions any agreement maximizes the product of net rents defined as the gains from cooperation relative to the disagreement outcome (e.g., see Binmore et al. 1986; Osborne and Rubinstein 1994). The required conditions are: invariance of the solution to monotonic transforms of utility, a fact that holds here given that the net rent functions of each municipality would likely not change structurally over time given the administrative nature of negotiation and the relatively short time periods involved; the impossibility of Pareto improvements should a bargaining solution exist, which is guaranteed by the definition of the objective function for our problem and the fact that governments would be bargaining on behalf of their residents; and independence of irrelevant alternatives. Independence of irrelevant alternatives is usually fairly stringent, but it holds in our problem since the net gains we define would mean that inefficient agreement points can be removed from consideration given that the agreement outcome by definition must improve net present value rents over the disagreement outcome, and this defines the contract set. As in most problems of this type, commitment on the part of both municipalities to the solution of the bargaining problem must hold. This is likely in our case because the negotiated agreement is between governments and thus a legal and administrative system exists to implement the solution that would be slow to change or difficult to circumvent.

  3. The results for the closed loop model are presented in the supplementary appendix. In the baseline model simulation, the social costs in the open loop model are 0.737 versus 0.542 in the closed loop model, which implies that the open loop model overstates the gains from bargaining by 3.2% in our application. These results are similar across sensitivity analyses.

  4. This assumption is simply one of convenience and implies that V(0), the net benefit to a municipality when it is infested but no transfer payment is received, is identical across municipalities. The model can be extended to reflect differences in tree cover and costs of control by differentiating this term across municipalities. This change affects the solution to the bargaining problem only by altering the disagreement outcomes in Eqs. (4)–(5), which affects the relative Hamiltonian weights in Eq. (12). The comparative insights developed later would not be affected by this additional complexity.

  5. In the case of emerald ash borer, the probability of spread is driven by the ovipositional preferences of the female beetle, which are proportional to the size of the pest population, the density of ash trees, and the prevalence of stressed, or vulnerable, ash trees (Mercader et al. 2011).

  6. If the path of spread was driven solely by, for example, the size of the pest population, N(t), it would be a straightforward extension of our model to specify population size as the model’s state variable using a probability of spread function given by P(N(t)). Other features of the model, such as the damage caused by the pest, could also be modified to depend on N(t).

  7. This growth function is a reduced form representation of the mechanics of the invasion that offers the benefit of generality. For a specific application, spread may be modeled explicitly to reflect case-specific dynamics of the pest and the host, as well as spatial characteristics of the problem, such as the distance between the two municipalities.

  8. We require commitment to exist here on the part of both municipalities. Not only is this easy to envision if municipalities are governments and transfers happen through administrative and legal procedures, but commitment has also been a common assumption in the bargaining literature. We also recognize that it may be the case that a transfer payment of the type proposed here would require a vote by inhabitants of the uninfested municipality, who may have different incentives to bargain than the government itself. In this case, the government is acting as a first-best planner (for its own citizens) and reduces the transaction costs of bargaining so that an agreement can be reached in the Coase spirit.

  9. It is possible that in some cases, the effectiveness of control, δ, is a declining function of the probability of spread, P(t). We do not model δ as endogenous in this study because doing so renders the theoretical model and our simulation approach intractable, and because it would require considerable data to calibrate the effect beyond some arbitrary assumption. Instead, we conduct a numerical sensitivity analysis in which we consider high and low values for δ. A comparison of the results between these two cases captures the intuition behind the effect of a decrease in δ as P(t) declines, ceteris paribus.

  10. Of all parameters in the model, this parameter, which is a technical coefficient that captures the relationship between a dollar spent on control and a reduction in the probability of spread, may be the one with the most uncertainty given that data concerning controls and invasive species population changes are not generally available. While it is not difficult to add uncertainty in this parameter, this would add little insight because this uncertainty would be common to both municipalities, and because spread is already probabilistic and is the most important aspect of the problem. Uncertain efficacy would simply be reflected in the already uncertain probability of spread.

  11. An infinite time horizon is unlikely given that the period of cooperation in the form of transfers would likely be limited by administrative mechanisms in each municipality.

  12. We assume that there is a close correspondence between the level of control and the transfer payment, and thus for simplicity we write net benefits as a function only of the transfer payment. For example, we could write the level of control as a function of the transfer payment, e(τ(t)), where e′ > 0. The net benefit function could then be written as V(e(τ(t))). Doing so complicates the notation without altering the results of the theoretical model.

  13. Although a closed-loop modeling approach could be used to allow renegotiation of the transfer payment in each period in response to updated information about whether the invasive species has spread, we use an open-loop approach in this analysis for several reasons. First, renegotiating a new transfer payment in each period for two municipalities likely involves high transactions costs. The results of our numerical simulation demonstrate that in many cases, such short-term agreements are unlikely to satisfy bargaining incentive constraints for both municipalities even without accounting for these transactions costs, so a longer-term agreement (modeled in the manner we choose) may be more viable in cases like that of the emerald ash borer. Second, because it is difficult to detect the arrival of emerald ash borer within the first 3–4 years after infestation, an annual reassessment of whether the pest has spread would be difficult to implement in practice. Finally, an open-loop formulation is appealing in terms of its ability to yield analytical insight into the bargaining transfer paths as is illustrated below.

  14. Because P(t) incorporates all pest control decisions prior to period t, the welfare function in period t also depends on all prior treatment control decisions.

  15. The path of transfer payments in (3) is outside of the expectation. This is reasonable in our empirical application given that it is difficult to detect whether the pest has spread over the relevant time horizon for a bargaining agreement (on the order of several years). Incorporating the transfer payment into the expectation here complicates the analytical expressions for the path of transfer payments under bargaining and the first-best outcomes. The difference in these two transfer payment paths, given by (18), remains analytically tractable but its increased complexity yields little additional insight into the problem.

  16. For simplicity \( \bar{V} \) is not time dependent. There is time dependence through many other channels that can affect the outcome of our bargaining game. The disagreement outcomes in (4) and (5) are in fact time dependent and will therefore change over time. Moreover, the agreement region of the problem, given in (7), is also time dependent. Including an additional time dependence through \( \bar{V} \) would complicate the problem, while adding little in terms of the intuition derived from the model.

  17. We do not consider the case in which two infested municipalities share in control costs. Because the municipalities are identical in all ways except for their initial state, they earn the same level of net benefits when they are infested.

  18. The disagreement outcome here is a corner solution in our model (see also Amacher and Malik 1998). It is in effect a pure free-riding solution for the uninfested municipality, which by doing nothing waits as long as possible before spending the cost of control.

  19. We might expect that the bargaining power held by the uninfested municipality would be relatively low if there is a high probability of spread from areas other than the adjacent infested municipality. For emerald ash borer, however, there is a small probability that the pest will spread to the uninfested municipality due to long-distance transport, but that probability is minor compared to the probability of spread from the adjacent municipality. As demonstrated by Kovacs et al. (2010), EAB tends to spread in a way that is consistent with an invasion front, rather than a more scattered pattern of spread.

  20. Specifically, these results require that the constraint set is convex and the objective functionals for both municipalities are concave over the constraint set. These assumptions hold given our assumptions about the shapes of f(P(t)) and V(τ(t)).

  21. Insecticides are most effective when their use is begun prior to infestation, though difficulty detecting adult beetles and early stages of infestation makes it hard to identify when to start treatments. Insecticide treatment is recommended if a tree is within 15–24 km of a known EAB infestation (Herms et al. 2014).

  22. Sander et al. (2010) find that the average homeowner in Dakota and Ramsey counties in Minnesota is willing to pay $1300 for a 10% increase in tree cover within 100 meters of their home and over $800 for a 10% increase in tree cover within 250 meters of their home. Assuming that each ash tree contributes $2100 of value to surrounding homes over a 30-year time horizon, and using a discount rate of 2%, the annualized net benefit of each ash tree is $94. This estimate is similar to that produced by the National Tree Benefit Calculator for a 15-inch diameter green ash tree. The Calculator yields an estimate of $147 in benefits from each ash tree each year to the residents of St. Paul (St. Paul Parks and Recreation 2015).

  23. In the simulation, we constrain P(t) to the interval [0, 1]. However, \( P(t) \le 1 \) is only. binding in the uncoordinated outcome with no transfer payment. It is straightforward to use a probability growth function that guarantees \( P(t) \le 1 \), such as the logistic growth function. We test a version of the model using the logistic growth function for the probability of spread, such that \( f(P(t)) = rP(t)(1 - P(t)/K) \) where K = 1. The change in the growth function has the greatest implications for the uncoordinated outcome, but the change in the path of transfer payments under the bargaining or first-best solutions is minimal. With the logistic function, the path of transfer payments in the bargaining solution is slightly higher, which drives the probability of spread to zero in as many as eight periods, as opposed to nine periods with the exponential growth function. Social costs under bargaining fall roughly 300,000 dollars with the exponential function compared to the logistic function. Additional simulation results are available upon request.

  24. It is necessary to solve this system of equations rather than the optimization problem directly in order to leverage the linearization of the Hamiltonian proposed by Ehtamo et al. (1988). Solving the bargaining problem directly, even numerically, is difficult because of the highly nonlinear nature of the multiplicative objective functional in (8).

  25. Selecting too short a time horizon reduces the chance of an agreement, because the benefit of the transfer payment is greatly reduced. Extending the time horizon further into the future has little effect on the nature of the bargaining outcome, which involves large payments to reduce the probability of spread early and declining payments thereafter to balance the present value of maintaining the stock of ash trees with the expected losses from spread. Furthermore, extremely lengthy agreements between municipalities are unlikely to be politically feasible. Our choice of T in the simulation balances these considerations.

  26. If δ is a function of \( P(t) \), e.g. \( \delta = \delta /P(t) \), the sensitivity analysis suggests that a decline in \( P(t) \) will put downward pressure on the path of transfer payments, resulting in lower total payments and a shorter path than in the case when δ is fixed.

References

  • Aadland D, Sims C, Finoff D (2015) Spatial dynamics of optimal management in bioeconomic systems. Comput Econ 45:545–577

    Article  Google Scholar 

  • Amacher GS, Malik AS (1998) Instrument choice when regulators and firms bargain. J Environ Econ Manag 35:225–241

    Article  Google Scholar 

  • Amacher GS, Ollikainen M, Koskela E (2012) Corruption and forest concessions. J Environ Econ Manag 63:92–104

    Article  Google Scholar 

  • Bhat MG, Huffaker RG (2007) Management of a transboundary wildlife population: a self-enforcing cooperative agreement with renegotiation and variable transfer payments. J Environ Econ Manag 53:54–67

    Article  Google Scholar 

  • Bhat MG, Huffaker RG, Lenhart SM (1993) Controlling forest damage by dispersive beaver populations: centralized optimal management strategy. Ecol Appl 3:518–530

    Article  Google Scholar 

  • Bhat MG, Huffaker RG, Lenhart SM (1996) Controlling transboundary wildlife damage: modeling under alternative management scenarios. Ecol Model 92:215–224

    Article  Google Scholar 

  • Binmore K, Rubinstein A, Wolinsky A (1986) The Nash bargaining solution in economic modeling. RAND J Econ 17:176–188

    Article  Google Scholar 

  • Büyüktahtakin İE, Haight RG (2017) A review of operations research models in invasive species management: state of the art, challenges, and future directions. Ann Oper Res. https://doi.org/10.1007/s10479-017-2670-5

    Google Scholar 

  • Calvo E, Rubio SJ (2012) Dynamic models of international environmental agreements: a differential game approach. Int Rev Environ Resour Econ 6:289–339

    Article  Google Scholar 

  • City of St. Paul (2014) Citywide EAB management strategies. https://www.stpaul.gov/departments/parks-recreation/natural-resources/forestry/disease-pest-management/citywide-eab. Accessed 6 March 2018

  • Cobourn KM, Burrack HJ, Goodhue RE, Williams JC, Zalom FG (2011) Implications of simultaneity in a physical damage function. J Environ Econ Manag 62:278–289

    Article  Google Scholar 

  • Ehtamo H, Ruusunen J, Kaitala V, Hamalainen RP (1988) Solution for a dynamic bargaining problem with an application to resource management. J Optim Theory Appl 59:391–405

    Article  Google Scholar 

  • Epanchin-Niell RS, Wilen JE (2012) Optimal spatial control of biological invasions. J Environ Econ Manag 63:260–270

    Article  Google Scholar 

  • Epanchin-Niell RS, Wilen JE (2014) Individual and cooperative management of invasive species in human-mediated landscapes. Am J Agric Econ 97:180–198

    Article  Google Scholar 

  • Epanchin-Niell RS, Hufford MB, Aslan CE, Sexton JP, Port JD, Waring TM (2010) Controlling invasive species in complex social landscapes. Front Ecol Environ 8:210–216

    Article  Google Scholar 

  • Feder G, Regev U (1975) Biological interactions and environmental effects in the economics of pest control. J Environ Econ Manag 2:75–91

    Article  Google Scholar 

  • Fiege M (2005) The weedy west: mobile nature, boundaries, and common space in the Montana landscape. West Hist Q 36:22–47

    Article  Google Scholar 

  • Frisvold GB, Caswell MF (2000) Transboundary water management: game-theoretic lessons for projects on the US–Mexico border. Agric Econ 21:101–111

    Google Scholar 

  • Gertler M, Trigari A (2006) Unemployment fluctuations with staggered Nash wage bargaining. In: NBER working paper 12498, national bureau of economic research, Cambridge, MA

  • Great Lakes Commission (2012) Restoring the natural divide: separating the Great Lakes and Mississippi River Basins in the Chicago area waterway system. https://www.glc.org/work/CAWS/reports. Accessed 6 March 2018

  • Grimsrud KM, Chermak JM, Hansen J, Thacher JA, Krause K (2008) A two-agent dynamic model with an invasive weed diffusion externality: an application to Yellow Starthistle (Centaurea solstitialis L.) in New Mexico. J Environ Manag 89:322–335

    Article  Google Scholar 

  • Hamalainen RP, Kaitala V, Haurie A (1984) Bargaining on whales: a differential game model with Pareto optimal equilibria. Oper Res Lett 3:5–11

    Article  Google Scholar 

  • Herms DA, McCullough DG, Smitley DR, Sadof CS, Cranshaw W (2014) Insecticide options for protecting ash trees from emerald ash borer, 2nd edn. North Central IPM Center, Urbana-Champaign, Illinois

    Google Scholar 

  • Koskela E, Schöb R (1999) Alleviating unemployment: the case for green tax reforms. Eur Econ Rev 43:1723–1746

    Article  Google Scholar 

  • Koskela E, Schöb R, Sinn H-W (1998) Pollution, factor taxation and unemployment. Int Tax Pub Financ 5:379–396

    Article  Google Scholar 

  • Kovacs KF, Haight RG, McCullough DG, Mercader RJ, Siegert NW, Liebhold AM (2010) Cost of potential emerald ash borer damage in U.S. communities, 2009–2019. Ecol Econ 69:569–578

    Article  Google Scholar 

  • Kovacs KF, Haight RG, Mercader RJ, McCullough DG (2014) A bioeconomic analysis of an emerald ash borer invasion of an urban forest with multiple jurisdictions. Resour Energy Econ 36:270–289

    Article  Google Scholar 

  • Liu Y, Sims C (2016) Spatial-dynamic externalities and coordination in invasive species control. Resour Energy Econ 44:23–38

    Article  Google Scholar 

  • Mazzanti M (2001) The role of economics in global management of whales: re-forming or re-founding IWC? Ecol Econ 36:205–221

    Article  Google Scholar 

  • McCullough DG, Mercader RJ (2012) Evaluation of potential strategies to SLow Ash Mortality (SLAM) caused by emerald ash borer (Agrilus planipennis): SLAM in an urban forest. Int J Pest Manag 58:9–23

    Article  Google Scholar 

  • Melo F (2014) In emerald ash borer fight, St. Paul sticks with strategy of removing trees. St. Paul Pioneer Press, Saint Paul, p 24

    Google Scholar 

  • Mercader RJ, Siegert NW, Liebhold AM, McCullough DG (2011) Influence of foraging behavior and host spatial distribution on the localized spread of the emerald ash borer, Agrilus planipennis. Popul Ecol 53:271–285

    Article  Google Scholar 

  • Minneapolis Park and Recreation Board (2014) Ash canopy replacement plan. https://www.minneapolisparks.org/_asset/3nrmra/terrestrial-eab-ash-canopy-replacement-plan.pdf. Accessed 6 March 2018

  • Munro GR (1979) The optimal management of transboundary renewable resources. Can J Econ 12:357–376

    Article  Google Scholar 

  • Nash JF Jr (1950) The bargaining problem. Econometrica 18:155–162

    Article  Google Scholar 

  • Olson LJ (2006) The economics of terrestrial invasive species: a review of the literature. Agric Resour Econ Rev 35:178–194

    Article  Google Scholar 

  • Osborne MJ, Rubinstein A (1994) A course in game theory. MIT Press, Cambridge

    Google Scholar 

  • Sander H, Polasky S, Haight RG (2010) The value of urban tree cover: a hedonic property price model in Ramsey and Dakota Counties, Minnesota, USA. Ecol Econ 69:1646–1656

    Article  Google Scholar 

  • Sims C, Aadland D, Finnoff D (2010) A dynamic bioeconomic analysis of mountain pine beetle epidemics. J Econ Dyn Control 34:2407–2419

    Article  Google Scholar 

  • St. Paul Parks and Recreation (2015) Emerald ash borer: frequently asked questions. http://www.stpaul.gov/DocumentCenter/View/78030. Accessed 6 March 2018

  • van der Ploeg F, de Zeeuw AJ (1992) International aspects of pollution control. Environ Resour Econ 2:117–139

    Article  Google Scholar 

  • Wilen JE (2007) Economics of spatial-dynamic processes. Am J Agric Econ 89:1134–1144

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Forest Resources and Environmental Conservation, Virginia Tech, 310 West Campus Drive, Blacksburg, VA, 24061, USA

    Kelly M. Cobourn & Gregory S. Amacher

  2. USDA Forest Service Northern Research Station, Saint Paul, MN, USA

    Robert G. Haight

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  1. Kelly M. Cobourn
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  2. Gregory S. Amacher
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  3. Robert G. Haight
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Correspondence to Kelly M. Cobourn.

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Cobourn, K.M., Amacher, G.S. & Haight, R.G. Cooperative Management of Invasive Species: A Dynamic Nash Bargaining Approach. Environ Resource Econ 72, 1041–1068 (2019). https://doi.org/10.1007/s10640-018-0238-8

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