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Cooperative game theory provides an appropriate framework to assess the likelihood of conflict resolution, encourage cooperation among parties, and determine each party's share in resource sharing conflicts. In calculating the fair and efficient allocation of the incremental benefits of cooperation, cooperative game theory methods often do not consider the exogenous bargaining powers of the players based on factors, that are external to the game, such as their political, economic, and military powers. This study reformulates three well-known cooperative game theory methods, namely, Nash-Harsanyi, Shapley, and Nucleolus, to account for the exogenous bargaining powers of the players in cooperative games. Using the Caspian Sea international conflict as an example, this paper shows how the negotiators' exogenous bargaining power can change the outcome of resource sharing games. The proposed weighted cooperative game theory approach can help determine practical resolutions for real-world conflicts in which the exogenous powers of players can have a significant influence on the outcome of negotiations. [ABSTRACT FROM AUTHOR]

Summary Reservoir systems with multiple operators can benefit from coordination of operation policies. To maximize the total benefit of these systems the literature has normally used the social planner’s approach. Based on this approach operation decisions are optimized using a multi-objective optimization model with a compound system’s objective. While the utility of the system can be increased this way, fair allocation of benefits among the operators remains challenging for the social planner who has to assign controversial weights to the system’s beneficiaries and their objectives. Cooperative game theory provides an alternative framework for fair and efficient allocation of the incremental benefits of cooperation. To determine the fair and efficient utility shares of the beneficiaries, cooperative game theory solution methods consider the gains of each party in the status quo (non-cooperation) as well as what can be gained through the grand coalition (social planner’s solution or full cooperation) and partial coalitions. Nevertheless, estimation of the benefits of different coalitions can be challenging in complex multi-beneficiary systems. Reinforcement learning can be used to address this challenge and determine the gains of the beneficiaries for different levels of cooperation, i.e., non-cooperation, partial cooperation, and full cooperation, providing the essential input for allocation based on cooperative game theory. This paper develops a game theory–reinforcement learning (GT–RL) method for determining the optimal operation policies in multi-operator multi-reservoir systems with respect to fairness and efficiency criteria. As the first step to underline the utility of the GT–RL method in solving complex multi-agent multi-reservoir problems without a need for developing compound objectives and weight assignment, the proposed method is applied to a hypothetical three-agent three-reservoir system. [ABSTRACT FROM AUTHOR]

Water allocation is a growing concern in a developing world where limited resources like fresh water are in greater demand by more parties. Negotiations over allocations often involve multiple groups with disparate social, economic, and political status and needs, who are seeking a management solution for a wide range of demands. Optimization techniques for identifying the Pareto-optimal (social planner solution) to multi-criteria multi-participant problems are commonly implemented, although often reaching agreement for this solution is difficult. In negotiations with multiple-decision makers, parties who base decisions on individual rationality may find the social planner solution to be unfair, thus creating a need to evaluate the willingness to cooperate and practicality of a cooperative allocation solution, i.e., the solution's stability. This paper suggests seeking solutions for multi-participant resource allocation problems through an economics-based power index allocation method. This method can inform on allocation schemes that quantify a party's willingness to participate in a negotiation rather than opt for no agreement. Through comparison of the suggested method with a range of distance-based multi-criteria decision making rules, namely, least squares, MAXIMIN, MINIMAX, and compromise programming, this paper shows that optimality and stability can produce different allocation solutions. The mismatch between the socially-optimal alternative and the most stable alternative can potentially result in parties leaving the negotiation as they may be too dissatisfied with their resource share. This finding has important policy implications as it justifies why stakeholders may not accept the socially optimal solution in practice, and underlies the necessity of considering stability where it may be more appropriate to give up an unstable Pareto-optimal solution for an inferior stable one. Authors suggest assessing the stability of an allocation solution as an additional component to an analysis that seeks to distribute water in a negotiated process. [Copyright &y& Elsevier]

Abstract: Post-Soviet legal governance regime of Caspian Sea – the largest inland body of water on earth – remains a source of conflict among the five coastal states of Azerbaijan, Iran, Kazakhstan, Russia, and Turkmenistan. Although different division methods have been suggested for sharing the sea and its valuable resources, the actual gain of the countries is unclear as the proposed methods focus either on the oil and gas or the areal share of the parties. The Caspian Sea Negotiation Support System (Caspian Sea NSS) is developed in this study to delineate optimal boundaries for sharing the sea through simultaneous consideration of the countries' areal and resource shares under different sharing methods. This NSS is a complex optimization model, with a solver engine that provides reliable results with a reasonable computational effort using a heuristic method. The model is run under different division scenarios to evaluate the sensitivity of each party's gain and locations of nautical boundaries to the division rules and the economic values of the resources. Results show a high sensitivity of the optimal nautical boundaries to the division rules and an indirect relationship between the allocated area and resource shares. The findings highlight the necessity for considering utility shares in negotiations as opposed to adopting areal division rules which ignore the utilities and might result in unfair resource allocation. The main policy implication of the study is that clarification of the countries' resource and areal gain under any suggested legal regime for governing the Caspian Sea is essential to the success of the negotiations. [Copyright &y& Elsevier]

Abstract: In a recent article in this journal entitled “Game Theory and Climate Diplomacy”, DeCanio and Fremstad (2013) provide an interesting treatment of a range of simple game theoretic characterizations of international climate negotiations. The authors use the Nash and Maxi-min stability definitions to analyze 25 two-by-two ordinal games, which they recognize as “possible game-theoretic characterizations of climate negotiations between two players (e.g., Great Powers or coalitions of states)”. The authors' main conclusion that the Prisoner's Dilemma might not be the best description of climate negotiations game is consistent with the findings of others who have studied two-by-two conflicts over natural commons (Bardhan, 1993; Madani, 2010; Sandler, 1992; Taylor, 1987). Nevertheless, given the importance of the climate change issue, as well as the potential effects of our actions on the state of the environment and the well-being of future generations, I would like to address some gaps in their analysis, which result in it having limited usefulness for policy purposes. Of course, all models are simplified representations of reality, full of limitations. “Essentially, all models are wrong, but some are useful” (Box and Draper, 1987). So, “the practical question is how wrong do they have to be to not be useful” (Box and Draper, 1987). Models' limitations need to be carefully considered when interpreting them or applying their results to policy but some models are too simple to provide useful policy advice. [Copyright &y& Elsevier]

Abstract: Game theory provides a useful framework for studying Multi-Criteria Decision Making problems. This paper suggests modeling Multi-Criteria Decision Making problems as strategic games and solving them using non-cooperative game theory concepts. The suggested method can be used to prescribe non-dominated solutions and also can be used as a method to predict the outcome of a decision making problem. Non-cooperative stability definitions for solving the games allow consideration of non-cooperative behaviors, often neglected by other methods which assume perfect cooperation among decision makers. To deal with the uncertainty in input variables a Monte-Carlo Game Theory (MCGT) approach is suggested which maps the stochastic problem into many deterministic strategic games. The games are solved using non-cooperative stability definitions and the results include possible effects of uncertainty in input variables on outcomes. The method can handle multi-criteria multi-decision-maker problems with uncertainty. The suggested method does not require criteria weighting, developing a compound decision objective, and accurate quantitative (cardinal) information as it simplifies the decision analysis by solving problems based on qualitative (ordinal) information, reducing the computational burden substantially. The MCGT method is applied to analyze California’s Sacramento-San Joaquin Delta problem. The suggested method provides insights, identifies non-dominated alternatives, and predicts likely decision outcomes. [Copyright &y& Elsevier]

Abstract: Cooperative game theory solutions can provide useful insights into how parties may use water and environmental resources and share any benefits of cooperation. Here, a method based on Nash and Nash–Harsanyi bargaining solutions is developed to explore the Federal Energy Regulatory Commission (FERC) relicensing process, in which owners of non-federal hydropower projects in the United States have to negotiate their allowable operations, with other interest groups (mainly environmental). Linkage of games to expand the feasible solution range and the “strategic loss” concept are discussed and a FERC relicensing bargaining model is developed for studying the bargaining stage (third stage) of the relicensing process. Based on the suggested solution method, how the lack of incentive for cooperation results in long delay in FERC relicensing in practice is explained. Further, potential effects of climate change on the FERC relicensing are presented and how climate change may provide an incentive for cooperation among the parties to hasten the relicensing is discussed. An “adaptive FERC license” framework is proposed, based on cooperative game theory, to improve the performance and adaptability of the system to future changes with no cost to the FERC, in face of uncertainty about future hydrological and ecological conditions. [ABSTRACT FROM AUTHOR]

Summary: Managing water resources systems usually involves conflicts. Behaviors of stakeholders, who might be willing to contribute to improvements and reach a win–win situation, sometimes result in worse conditions for all parties. Game theory can identify and interpret the behaviors of parties to water resource problems and describe how interactions of different parties who give priority to their own objectives, rather than system’s objective, result in a system’s evolution. Outcomes predicted by game theory often differ from results suggested by optimization methods which assume all parties are willing to act towards the best system-wide outcome. This study reviews applicability of game theory to water resources management and conflict resolution through a series of non-cooperative water resource games. The paper illustrates the dynamic structure of water resource problems and the importance of considering the game’s evolution path while studying such problems. [Copyright &y& Elsevier]