Location choice for renewable resource extraction with multiple non-cooperative extractors: a spatial Nash equilibrium model and numerical implementation

Abstract

Especially in lower-income countries, the distribution of renewable resources in open access settings often reflects the non-cooperative spatial extraction decisions of many individuals who spread out across a landscape. These individuals recognize tradeoffs between distance to the resource, density, and competition amongst extractors. In this paper we present a game theoretic model that explicitly accommodates such explicitly spatial non-cooperative behavior with respect to the extraction of a stationary renewable natural resource, such as a non-timber forest products or bivalvia (for example, oysters, clams), that is located in a two dimensional landscape. Villagers that have identical labor allocations and preferences are shown to undertake very different extraction pathways in equilibrium. For example, some may extract in more congested patches closer to the village while others may extract in less crowded but more distant patches. For many parameterizations, we find multiple spatial Nash equilibria that differ with respect to the number of villagers at each resource location, whether individual villagers extract from one or multiple locations, and the extent and spatial pattern of resource degradation. In addition to finding equilibria with widely different actions taken by identical extractors, the analysis here demonstrates the impact of simplifying assumptions for spatial decisions on predictions of policy impact, resource distributions, and conflict.

Optimal Siting, Sizing, and Enforcement of Marine Protected Areas

“…Still, total fisher effort is being allocated across space in this framework, and in much the same way that effort is distributed in models that allocate effort across space to meet rent dissipation without considering decisions-including a site decision-and without considering distance fixed costs and labor tradeoffs. Related models with extraction site choices demonstrate that extractors become one-site specializers in the presence of large enough distance costs; our constraint of a one site choice corresponds to a setting with significant distance costs (Sterner et al 2018). Other related research explores multiple extraction sites (Albers et al 2019).…”

Spatial protected area decisions to reduce carbon emissions from forest extraction

“…The intractability necessitates the need for numerical methods to solve this problem. With similarities to Sterner, et al (2018), the solution method uses iterated best response to find the long run non-cooperative Nash equilibrium of labor allocation and extraction location decisions in pure strategies. Within the spatial landscape, ten basic villager strategy types, in terms of location and number of patches from which to extract, emerge.…”

“…After each period, the forest regenerates. We repeat this process until resource stocks and labor allocations show a stable repeating pattern that forms a steady state, which we use for analysis here (see Sterner et al 2018 for further description of a similar solution method to the same model without the manager).…”

“…The outputs of the model presented are in the steady state when harvest equals growth and consist of the stock of the resource in each patch and each individual villager's income. The model of villagers and their interactions here is identical to the model explored in Sterner et al (2018) and the development of the model below draws from that paper.…”

“…Here, we use the model of the uncoordinated villager spatial forest extraction decisions of in a spatial Nash equilibrium from Sterner, et al (2018) to reflect these characteristics of villager extraction decisions. The solution method here differs from Sterner et al, holding similarities with other models such as Bayer and Timmins (2005) and Timmins and Murdock's (2007) spatial Nash bargaining game.…”