What makes water resources a natural candidate for cooperative game theory applications

"Indeed this is a question that intrigues many scholars involved in this field. First, water-related conflicts involve usually a small number of stakeholders (players) that are interrelated to each other. Therefore, there is a greater scope for strategic behavior among players in water-related conflicts. Second, the level of externalities associated with water utilization is a big incentive to cooperate. Externalities include (a) the zero-sum (or constant-sum) outcomes of unilateral use of the resource (e.g., if party B uses more of the resource in the aquifer, less is left to party A, and also the cost of pumping party A faces is much more substantial due to the depth to the water table), and (b) the negative impact of water quality degradation that party A—the upstream— imposes on party B—the downstream (in the case of a river). Third, the great economies of scale associated with water infrastructure make it more attractive to build bigger rather than smaller water projects, hence providing incentives to joint considerations. Fourth, water projects are in many cases multi-objective ones, leading to inclusion interests. Therefore, a major issue of water projects investment and management is the allocation of the cost and benefits among the various stated project objectives (e.g., sub-sectors, groups of beneficiaries). And fifth, many water problems are transboundary in nature, leading to inter-jurisdictional, interregional, or international conflicts. Since the players and the problems will last, it is likely that cooperation may be attractive for part or all the players." (See additional discussion in Chapters 5, 6, 7, and 10.)

The compelling reason for the application of game theory to environmental and natural resource problems is that these problems stem from interdependence among agents, through their interrelated actions and strategies. Not only are the outcomes of decisions by agents interrelated, but also individual decisions are often taken without knowledge of the decisions of other agents (see box above for the case of water resources).

The public good aspects of natural resources at local or global scales, and the externalities associated with them, make their management challenging, as there are incentives to free riding. Sustainable management calls for control mechanisms designed to induce collective action and cooperation among stakeholders.

There are many examples of lack of enforcement by authorities or absence of any authority; for example, in the cases of carbon emissions, air quality, water resource quantity and quality (especially for groundwater), and loss of biodiversity and natural capital. And when enforcement is in place, there are also problems of asymmetric information between the regulatory agency and the agents using the resource.

Game theory demonstrates that under noncooperative solutions, each individual agent maximizes its own benefit taking into account that other agents also maximize their individual benefits. Noncooperation is driven by the structure of incentives, theoretical dimensions of which include the prisoner's dilemma game, the so-called tragedy of the commons, and free riding (Axelrod 1984; Hardin 1968).

Cooperative solutions could result from binding agreements with built-in penalties that are enforced by the agents themselves, called self-enforcing agreements. In such a setting, a characteristic function is defined that computes for each coalition of players the total benefits that all members of the coalition can attain by themselves. The best-known noncooperative game solution is the Nash equilibrium of the game, while the full cooperation game solution maximizes the coalition payoff, in which case the agents have to find a reasonable distribution of the additional benefits obtained from cooperation. These points are demonstrated in Figure 1.1, using economic concepts that are applied to a problem of pollution abatement.

Figure 1.1 depicts a situation of pollution abatement where linear marginal benefit and cost functions are assumed. MBi are marginal benefits and MCi are marginal costs from pollution abatement by each player i, and MB are total marginal benefits from abatement. Under A0, the noncooperative state, there is no effort by players on pollution abatement. The noncooperative solution ANC is the Nash equilibrium where players equalize individual marginal benefits MBi with individual marginal costs MCi. The level of abatement in the full cooperative solution AC maximizes welfare and applies the condition for efficient provision of public goods MB = £iMBi = MC. The specification of the marginal benefit function requires knowledge of biophysical processes and pollution damages to ecosystems. When this information is not available, the optimum level of abatement AC is not known. In

Figure 1.1 Pollution abatement under noncooperative and cooperative solutions.

such a case the alternative is to establish an abatement threshold AT, where cooperation implies minimizing total abatement costs across players to reach the threshold.1

Full cooperation is not usually an equilibrium because of possible free riding by some players, and also because some players may end up being worse off due to the nature of the cooperative solution and their relatively good status quo situation. To make sure that all players improve upon the individual Nash equilibrium solution, gains could be redistributed through side payments. This is the usual outcome of partial cooperation in real-world situations, which involve both cooperating and free-riding players, and where negotiations lead to agreements with built-in incentives that reward or penalize individuals joining or disrupting the agreement.

Several mechanisms have been suggested to redistribute gains among players. In practice, allocation mechanisms are frequently based on equity rules, which are a type of social norm. Percentage reductions in emissions have been applied in the Montreal and Kyoto Protocols, and percentage allocation of resources is embodied in many water resource agreements to reduce water extractions or to share river flows. Other allocation mechanisms include the Shapley value, Nash bargaining, and cost-sharing rules. These will not be explained here.

Cost-sharing rules could be implemented using taxes, tradable permits and lump sum fines or subsidies. In the case of pollution, side payments may contradict the polluter pays principle as pollution abatement may require compensation to polluters, and also anticipated side payments may induce abatement efforts below noncooperation.

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