THE EFFECTS OF DIFFERENT STRATEGIC VARIABLES IN NONCOOPERATIVE FISHERIES GAMES

Abstract In this paper, we use stock size, harvest quantity, and fishing effort as strategic variables. We model a two‐agent noncooperative fishery game, where the agents (nations) harvest a common fish stock. The planning horizon is infinite. The model is solved successively using one instrument at a time as the strategic variable in the game. The net present values of fishing and the escapement stock level from the three different models are compared to show how the choice of variables affects the results. The choice of strategic variable is not a trivial one, as the results are shown to be sensitive to the discounting, the stock's rate of growth, and the assumptions about the distribution of the fish in response to harvesting.     

NONCOOPERATIVE MANAGEMENT OF THE NORTHEAST ATLANTIC COD FISHERY: A FIRST MOVER ADVANTAGE

The point of departure for this analysis is Bjørndal and Lindroos [2012], who developed an empirical bioeconomic model to analyze cooperative and noncooperative management of Northeast Atlantic cod. In their analysis, only constant strategies were analyzed for noncooperative games. In this paper, nonconstant strategies are considered. Moreover, the fishery in question is characterized by cooperative management. What may happen in the real world is that one nation breaks the cooperative agreement by fishing in excess of its quota. Often, it takes time for the other agent to detect this and respond. In this paper, we allow this kind of delayed response into a two‐agent noncooperative game so that, if country 2 exceeds its quota, there will be a time lag before this is detected by country 1; moreover, there may also be a delay until country 1 is able to respond. Results show that the outcome critically depends on the length of these two lags as well as initial conditions.     

The structure of optimal solutions for harvesting a renewable resource

We consider the problem of optimal harvesting of a renewable resource whose dynamics are governed by logistic growth and whose payoff is proportional to the harvest. We consider both the case of a finite and an infinite time horizon and analyse the structure of the optimal solutions and their dependence on the parameters of the model. We show that the optimal policy can only have one of three structures: (1) maximal harvesting effort until the resource is depleted, (2) zero harvesting during an initial time interval followed by a subsequent switch to maximal harvesting effort, or (3) a singular solution, which corresponds to an intermediate level of harvesting, accompanied by the most rapid approach path. All three scenarios emerge, with minor variations, with finite and infinite time horizons, depending on the particular combination of parameters of the system. We characterize the conditions under which the singular solution is optimal and present suggestions for designing an optimal and sustainable harvesting strategy. Recommendations for Resource Managers :

• We have rigorously explored a standard optimal harvesting model and its steady states.
• We show that three different types of solutions may emerge: (i) maximal harvesting eventually leading to a complete depletion of the stock; (ii) maximal harvesting with a potential period of idleness leading to a positive stock; (iii) an initial phase of either no or full harvesting followed by a period of intermediate harvesting intensity leading to a positive stock (singular solution).
• With some modifications, similar results hold for a finite planning horizon.
• Which of these three scenarios emerges in the finite horizon case depends not only on the parameter values but also on the length of the planning horizon.

     

HUMAN FERTILITY DECISIONS AND COMMON PROPERTY RESOURCES: A DYNAMIC ANALYSIS

ABSTRACT. In rural areas of developing countries, parental decisions on number of offspring may be made on the basis of the role of children in harvesting local common property renewable resources. It has been argued that this may lead to a cycle of human over‐population and resource over‐exploitation. To investigate the plausibility of this argument, we present a discrete dynamic model with two state variables representing human population level N and resource stock level S. The model is similar to one given by Nerlove and Meyer but differs in several important respects. It is assumed that, in each over‐lapping generation of parents and children, parents decide how many children to have based on their resulting share of the local resource harvest and the costs associated with child‐rearing. Using simulation and analytical methods, the long term steady state population and resource stock levels for this dynamic noncooperative game are contrasted with the steady state when parental fertility decisions are made in a cooperative manner.     

OPTIMAL RECOVERY OF A SHARED RESOURCE STOCK: A DIFFERENTIAL GAME MODEL WITH EFFICIENT MEMORY EQUILIBRIA

We consider an optimal two-country management of depleted transboundary renewable resources. The management problem is modelled as a differential game, in which memory strategies are used. The countries negotiate an agreement among Pareto efficient harvesting programs. They monitor the evolution of the agreement, and they memorize deviations from the agreement in the past. If the agreement is observed by the countries, they continue cooperation. If one of the countries breaches the contract, then both countries continue in a noncooperative management mode for the rest of the game. This noncooperative option is called a threat policy. The credibility of the threats is guaranteed by their equilibrium property. Transfer or side payments are studied as a particular cooperative management program. Transfer payments allow one country to buy out the other from the fishery for the purpose of eliminating the inefficiency caused by the joint access to the resources. It is shown that efficient equilibria can be reached in a class of resource management games, which allow the use of memory strategies. In particular, continuous time transfer payments (e.g., a share of the harvest) should be used instead of a once-and-for-all transfer payment.     

THE EFFECTS OF ITQ IMPLEMENTATION: A DYNAMIC APPROACH

ABSTRACT. This paper investigates the intertemporal effects of introducing Individual Transferable Quota, ITQ, fishery management programs on stock size, fleet size and composition, and returns to quota holders and to vessel operators. Theoretical analysis is conducted using a specific version of a general dynamic model of a regulated fishery. It is demonstrated that the effects will differ depending upon the prevailing regulation program, current stock size, and existing fleet size, composition and mobility and upon how the stock and fleet change over time after the switch to ITQs. The paper expands upon previous works by modeling the dynamics of change in fleet and stock size and by allowing for changes in the TAC as stock size changes, by comparing ITQs to different regulations, and by allowing the status quo before ITQ implementation to be something other than a bioeconomic equilibrium. Specific cases are analyzed using a simulation model. The analysis shows that the annual return per unit harvest to quota owners can increase or decrease over the transition period due to counteracting effects of changes in stock and fleet size. With ITQs denominated as a percentage of the TAC, the current annual value of a quota share depends upon the annual return per unit of harvest and the annual amount of harvest rights. Because the per unit value can increase or decrease over time, it is also possible that the total value can do the same. Distribution effects are also studied and it is shown that while the gains from quota share received are the present value of a potentially infinite stream of returns, potential losses are the present value of a finite stream, the length of which depends upon the remaining life of the vessel and the expected time it will continue to operate.     

MANAGING HARVESTING TO MINIMIZE THE IMPACT OF EPIDEMICS ON WILD FISH STOCKS

ABSTRACT. Epidemic diseases inflict substantial damage to stocks of harvested species. Epidemic waves can be predictable away from their origin. I use a classical epidemiology model to investigate the interaction of harvesting strategy with an epidemic. The effect of reducing populations by harvesting before the epidemic depends upon the nature of the epidemic's survivors. If these have recovered following infection, then pre‐epidemic fishing optimizes the harvest, but reduces long‐term survival. However, if these survivors avoided infection, then increased pre‐epidemic fishing effort can increase post‐epidemic populations; survival is maximized by reducing the pre‐epidemic population to the threshold required to propagate infection. Post‐epidemic harvesting provides poor returns and damages stocks. Optimal stock management strategy in the face of a predicted epidemic depends upon balancing harvesting and conservation of stocks complimentary or antagonistic goals, depending on the nature of the epidemic.     

Two noncooperative games between a coalition and its surrounding in a class of n-person games with constant sum

A cooperative game engendered by a noncooperative n-person game (the master game) in which any subset of n players may form a coalition playing an antagonistic game against the residual players (the surrounding) that has a (Nash equilibrium) solution, is considered, along with another noncooperative game in which both a coalition and its surrounding try to maximize their gains that also possesses a Nash equilibrium solution. It is shown that if the master game is the one with constant sum, the sets of Nash equilibrium strategies in both above-mentioned noncooperative games (in which a coalition plays with (against) its surrounding) coincide.     

A fair and time‐consistent sharing of the joint exploitation payoff of a fishery

We consider the problem of efficiently managing a fishery where pollution externalities are present. The open‐access bionomic model is analyzed in an ‐player differential game framework with two‐state variables, that is, the fish stock and the pollution stock. We characterize the noncooperative feedback‐Nash equilibrium and cooperative solution, and define an egalitarian sharing rule to allocate the joint welfare maximizing payoff over an infinite time horizon, and show that this rule is time consistent. Recommendations for Resource Managers

• ● Cooperation in management of a fishery where pollution externalities are present yields a higher payoff over time as compared to the noncooperative behavior.
• ● The dividend of cooperation can be allocated among the fisherpersons according to an egalitarian sharing rule.
• ● This allocation is time‐consistent, that is, no player will be tempted to deviate from cooperation as time goes by, and the initial agreement is sustainable.

     

Optimal harvesting in a predator-prey model with Allee effect and sigmoid functional response

This work deals with the determination of the optimal harvest policy in an open access fishery in which both prey and predator species are subjected to non-selective harvesting.The model is described by autonomous ordinary differential equation systems, the functional response of the predators is Holling type III and the prey growth is affected by the Allee effect. The catch-rate functions are based on the catch per unit effort (CPUE) or Schaefer’s hypothesis.The problem of determining the optimal harvest policy is solved by using Pontryagin’s maximal principle. The problem here studied is to maximize a cost function representing the present value of a continuous time-stream of revenue of the fishery.     

Time-limited pest control of a Lotka–Volterra model with impulsive harvest

A kind of time-limited pest control of a Lotka–Volterra model with impulsive harvest, described by the initial and boundary value problem of impulsive differential equation, is presented. The aim of pest control can be achieved if the model has a solution, otherwise the aim cannot be achieved. By the comparison principle, the conditions under which the model has a solution are found by a series of the upper solutions and the conditions under which the model has no solution are also given by a series of the lower solutions. Furthermore, if the other parameters are given, the times of harvesting pest in the given time is estimated. The theoretical results and the numerical simulations show that the density of the natural enemy will decrease when the pest decreases although the control measures to the pest do not directly affect the natural enemy. Finally, some discussions are given.     

COMPARING PROACTIVE AND REACTIVE MANAGEMENT: MANAGING A TRANSBOUNDARY FISH STOCK UNDER CHANGING ENVIRONMENT

Environmental change in general, and climate change in particular, can lead to changes in distribution of fish stocks. When such changes involve transboundary fish stocks, the countries sharing the stock need to reconsider their harvesting policies. We investigate the effects of changing stock distribution on the optimal fishing policies in a two players’ noncooperative game. We compare reactive management, under which the manager ignores future distributional shifts (knowingly or unknowingly), with proactive management where the manager considers such shifts in his decisions. A dynamic programming model is developed to identify closed‐loop Nash strategies. We show that the role of two players is symmetric under reactive management but asymmetric under proactive management where managers anticipate future changes in stock ownership. The player losing the stock tends to harvest more aggressively compared to the player gaining the stock who acts more conservatively. Strategic interactions show tendency for complementary actions that can change abruptly during the ownership transition. The differences between management regimes vary from quantitative to qualitative; differences are minimal for stocks with little or no schooling, whereas highly schooling stocks may avoid collapse only under proactive management.     

Bargaining on whales: A differential game model with pareto optimal equilibria

A two-country differential game model of whaling is used for analysing a dynamic bargaining problem. At a given initial time, the two countries may either continue on a noncooperative mood of play characterized by an open-loop Nash-equilibrium, or negotiate a bargaining solution which we define as the Kalaï-Smorodinsky solution. The cooperative solution calls for a restraint in the whaling efforts which leaves a temptation to cheat for any player. The model shows how, by announcing a credible threat, namely to make whaling an ‘open-access’ fishery, a country can eliminate this temptation to cheat and transform the cooperative solution into an equilibrium.     

A cost allocation problem arising in hub–spoke network systems

This paper studies a cost allocation problem arising from hub–spoke network systems. When a large-scale network is to be constructed jointly by several agents, both the optimal network design and the fair allocation of its cost are essential issues. We formulate this problem as a cooperative game and analyze the core allocation, which is a widely used solution concept. The core of this game is not necessarily non-empty as shown by an example. A reasonable scheme is to allocate the cost proportional to the flow that an agent generates. We show that, if the demand across the system has a block structure and the fixed cost is high, this cost allocation scheme belongs to the core. Numerical experiments are given with real telecommunication traffic data in order to illustrate the usefulness of our analytical findings.     

Resource Dynamics under Partial Cooperation in an Oligopoly

We study the long-run evolution of a renewable resource which is subject to harvest by partially cooperating players who sell the harvested quantities on distinct markets. We derive explicit expressions for the total harvesting quantity of all players in this general framework and investigate the dependence of the total and relative harvest rates on the level of cooperation, available fish stock, and fishing costs. Combining the biological growth model with oligopoly leads to a nonlinear dynamic law for the evolution of the fish stock in the presence of commercial fishing. We provide also existence results for its equilibrium and examine the asymptotic behavior of the equilibrium. We are grateful for the critical comments and suggestions of three anonymous referees.     

Problems Involving Infrequent but Significant Contingencies

Problematic situations often arise in which it is required to provide a solution which will tend to avoid events, which, if they occur, would be very costly, or, if not directly costable, they would be highly undesirable. Although direct approaches to this sort of problem exist, they can be unmanageable. If, however, we take as a posit, that the frequency with which the undesirable events arise, in the optimum solution, is small, considerable simplifications can be made. Naturally we need to check the posit once the solution has been found. This paper considers three applications of this principle, viz. determination of how many chargers are needed for steel furnaces, where the undesirable event is “a furnace waits for service”; determination of the number of emergency beds to set aside in a hospital unit, where the undesirable event is “an emergency case arrives and no bed is immediately available”; determination of an inventory reorder rule where the undesirable event is “stock run-out”. The general principle is formalized.     

COMPETITION AND COOPERATION IN A DYNAMICAL MODEL OF NATURAL RESOURCES

Abstract In this paper, we propose a model describing the commercial exploitation of a common renewable resource by a population of strategically interacting agents. Players can cooperate or compete; cooperators maximize the payoff of their group while defectors maximize their own profit. The partition of the players into two groups, defectors and cooperators, results from the players' choices, so it is not predetermined. This partition is decided as a Nash equilibrium of a static game. It is shown that different types of players can exist in an equilibrium; more precisely, depending on the parameter values such as resource stock, cost, and so on, there might be equilibria only with defectors, cooperators, or with a combination of cooperators and defectors. In any case the total harvest depends on the renewable resource stock, so it influences agents' positions. It is assumed that at each time period the agents harvest according to Nash equilibrium, which can be combined with a dynamic model describing the evolution of fish population. A complete analysis of the equilibria is presented and their stability is analysed. The effect of the different Nash equilibria on the stability of the fish stock, showing that full cooperation is the most stable case, is examined.     

OPTIMAL FISH HARVESTING FOR A POPULATION MODELED BY A NONLINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATION

As the human population continues to grow, there is a need for better management of our natural resources in order for our planet to be able to produce enough to sustain us. One important resource we must consider is marine fish populations. We use the tool of optimal control to investigate harvesting strategies for maximizing yield of a fish population in a heterogeneous, finite domain. We determine whether these solutions include no‐take marine reserves as part of the optimal solution. The fishery stock is modeled using a nonlinear, parabolic partial differential equation with logistic growth, movement by diffusion and advection, and with Robin boundary conditions. The objective for the problem is to find the harvest rate that maximizes the discounted yield. Optimal harvesting strategies are found numerically.     

一类可再生资源系统的最优动态平衡收获

研究一类可再生资源系统的最优利用问题．首先,引进一个新的效用函数, 它依赖于收获努力度和资源量,由此导出最优控制问题．其次证明该控制问题最优解的存在性．然后,利用无穷区间上控制问题的最大值原理,得到一个非线性的四维最优系统．通过对上述系统正平衡解的详细分析,借助 Hopf 分支定理证明了极限环的存在性．之后考虑中心流形上的简化系统, 分析极限环的稳定性．最后,解释所得结果的生物经济学意义．