بهره برداری از منابع تجدید پذیر با فن آوری های متفاوت :تجزیه و تحلیل تکاملی

In this paper, we propose a dynamical model of technology adoption for the exploitation of a renewable natural resource. Each technology has a different efficiency and environmental impact. The process of technology adoption over time is modeled through an evolutionary game employed by profit maximizing exploiters. The loss in profits due to lower efficiency levels of environmentally-friendly technologies can be counterbalanced by the higher consumers’ propensity to pay for greener goods. The dynamics of the resource take place in continuous time, whereas the technology choice can be revised either in continuous-time or in discrete-time. In the latter case, the model assumes the form of a hybrid system, whose dynamics is mainly explored numerically. We shows that: (1) overexploitation of the resource arises whenever the reduction in harvesting due to a lower efficiency of clean technology is more than compensated by a higher propensity to pay for greener goods; (2) the difference between the fixed costs of these technologies can be exogenously fixed to provide an incentive for adopting clean technology without affecting the long-run level of the resource; and (3) in some cases, discrete switching of the technology causes overshooting in the dynamics whereas in others it enhances the stability of the system.

A main issue in the exploitation of common property resources is the so-called “stock externality”: individual exploiters do not take into account the effects of their current catch on the resource and on its future abundance. The non-coincidence between individual optima and collective optima is commonly referred to as the “tragedy of the commons”, after [21], and characterizes the exploitation of almost all shared natural resources, see also [13] and [28]. Moreover, enforcing control on the resource is a very difficult and often an ineffective task. In this paper, we address a descriptive model for the exploitation of a common pool renewable resource, on which the regulator does not enforce any restraint. However, some exploiters can decide to employ a less efficient but more “environmentally-friendly” technology if the loss in efficiency is counterbalanced by a higher price that consumers might be willing to pay for the greener product.1 The choice of the technology, which is an exogenous component of the model,2 only depends on the agents’ assessment on expected profits and not on ethical or environmental concerns, as agents are assumed to be selfish profit maximizers. Exploiters have to make two choices over time: which technology to adopt and, given that, the quantity to harvest. With respect to the problem of technology adoption, we model it through an evolutionary game in the spirit of [24] and [34], as is customary in natural resource exploitation models, see, among others, [32], [36], [1], [8] and [9]. Thus, agents can switch from the selected technology to another that is available if they expect that the change can be profitable. Regarding the quantities to be harvested, we follow [32] and assume that agents choose their catches continuously in order to be in a Nash equilibrium at any given time. We first address the case in which the choice of the technology can be revised continuously. This step constitutes a useful benchmark to understand the main qualitative properties of the model. Then we break down this assumption to conceive a scenario that is more similar to what could take place in a more realistic setting. In fact, changing technology immediately is not feasible in practical cases for different reasons, the most obvious of which is due to the interval of time required to conclude a single harvesting operation. Thus, it is natural to assume that only after a certain time interval may a change in the employed technology take place. In this circumstance the system can be modeled mathematically through a hybrid model, including continuous-time resource growth and impulsive changes of strategies. The latter takes place at discrete points in time according to an evolutionary endogenous switching mechanism. In recent years, hybrid dynamical systems have been widely employed for studying real-world problems in several branches of applied mathematics, such as engineering, biology and biomedical science (see e.g. [11], [12], [3], [18], [19] and [20]). In fishery models, hybrid systems have been recently proposed in [6] and [7]. The first goal of this paper is to gain an understanding of the influence of the length of the switching interval on the dynamics of the natural resource and profits. In some cases, continuous technology switching just speeds up the convergence to the same attractor of the hybrid system. In others, discrete switching and continuous switching exhibit different long-run behaviors. Interestingly, under some circumstances discrete switching may even introduce a stabilizing effect in the model because of more inertia in the system when switching decisions are based upon past profits. Another aim of the paper is to assess whether an unregulated use of the resource can be sustained in the long-run. Although this is true in some cases, we show some examples where every agent tends to use the less-efficient technology but the level of the resource in the long run is lower than the level obtained if every agent would have used the traditional technology. This occurs whenever the high price for the green product induces too many exploiters to over-harvest it. In these cases, the market itself is not able to mitigate the effects of the tragedy of the commons but additional regulatory policies must be introduced. For instance, a regulator could avoid poverty traps by providing an incentive for adopting a technology over the other. Analytic and numerical analysis show that the stability of equilibria is quite sensible to the difference in the fixed costs between the two available technologies but the level of harvesting is not affected by this difference. As a result, a regulator can employ the difference in fixed costs to steer the system towards the preferred long-run level of the resource. The problem of adopting a less efficient but more environmentally-friendly technology is motivated by some real-world cases occurring in fisheries outside exclusive economic zones. In this respect, a well-known example regards the landing of yellowfin tuna and the marketing of “dolphin safe” labels.3 Dolphins commonly swim together with tunas, but closer to the surface. Therefore fishing boats spot dolphins more easily than tuna. Consequently, although dolphins are a non-target species and have no commercial value, they have been largely captured as bycatch in tuna fisheries. Netting dolphins with tunas has severely endangered the population of dolphins. This issue motivated the introduction in the late 20th century of the “dolphin safe” labels in several countries such as the U.S., the U.K. or New Zealand.4 The presence of bycatch-free labels created market segmentation with different prices for labeled and non-labeled tuna cans. The model proposed in this paper can be regarded as a stylized version of this problem, but with appropriate adjustments it can be easily adapted to describe other real-world cases. This paper is structured as follows. Section 2 introduces the bioeconomic model. Section 3 is devoted to the analysis of the model with evolutionary switching of harvesting technologies in continuous-time and introduces a formulation of the model with continuous-time growth of the resource and discrete switching of technologies. Section 4 proposes several numerical analysis comparing the (transient and long-run) dynamic properties for the two models, also briefly addressing some policy measures to avoid poverty traps and stimulate the adoption of the environmentally-friendly technology. Section 5 concludes.

In this paper, we have studied a dynamical model of technology adoption for the exploitation of a renewable resource. Technology adoption is modeled through an evolutionary game, where agents can change strategies (i.e. the employed technology) continuously or at specified times. In the latter case the mathematical description of the system gives rise to a hybrid model. Similarities and differences between the two possible dynamical systems are outlined in this paper, mainly through numerical simulations. Continuous switching in general amplifies the final outcomes of the system in both negative and positive cases. Despite the fact that discrete-time replicator models are known to generate more complicated behaviors than those of a continuous-time (see, e.g. [35]), we showed several examples in which discrete switching may have a stabilizing effect: in fact, a form of inertia is introduced in the system when agents assess the fitness of each strategy according to the moving average of past profits over an interval of time. Overall, with continuous-time switching or with discrete-time switching and low switching propensity, the system is likely to be trapped in basins of non-optimal attractors. This occurs when other attractors of the system could guarantee more profits in the long-run. This comparison can be established by solving an intertemporal profit maximization problem with the same harvesting functions employed by the myopic agents. The numerical results suggest that the inner equilibrium of the hybrid model is destabilized whenever the corresponding inner equilibrium of the continuous model has complex conjugate eigenvalues with negative real part or for high enough values of the intensity of choice. Hence, when the equilibrium in the continuous model is a stable focus, the value of the intensity of choice in the hybrid model is likely to play a crucial role in the long-run dynamics of the system. The results confirm pretty intuitive and common sense concepts in natural resource modeling as well as some aspects of the problem that are less intuitive. In most cases higher immediate profits entail less welfare in the long run, because of “resource externalities”. A high willingness to pay for the “greener” product can indeed lead to over-harvesting and resource depletion, although the use of environmentally-friendly technology is prevalent. Our examples suggest that one does not only have to harvest differently, but also to harvest less. The market is not able to self-regulate in these delicate issues and, due to path dependence of the system, it is likely to be “locked-in” in sub-optimal outcomes. Bycatch-free labels could be an important example to follow, but it is also necessary to reduce total catches (at least in the short-run), to establish no-take zones (on this point see [17], [27] and [5]) and to integrate the control of exploitation activities with the dynamics of the whole ecosystem (reduction of bycatch and pollution). One possible extension of the model is to explicitly consider the bycatch dynamics and to study the condition for the sustainable exploitation of the target and non-target species under different assumptions on their relationship (predator-prey, symbiotic interaction or negative interaction). In addition, it would be interesting to study the evolutionary model with switching costs, as indicated in Appendix A.