2006年-世界发展银行全球_Cooperative_Game_Theory_and_its_Application_to_Natural_Environmental_and_Water_Resource_Issues___1_Basic_Theory_30页_425kb

Summary of WPS4072: Cooperative Game Theory and Its Application to Natural, Environmental and Water Resource Issues

Core Content

This working paper provides an introduction to Cooperative Game Theory (CGT) and its application to natural, environmental, and water resource issues. The paper is part of a series exploring the use of CGT in development and environmental contexts.

The paper emphasizes that CGT models focus on the results of cooperation, rather than the strategic stages leading to coalition formation. It discusses how CGT aims to determine which coalitions can be formed and how to divide the gains of these coalitions in a way that ensures a sustainable agreement. The central idea is the equitable and fair sharing of cooperative gains, which is a key aspect of CGT solution concepts.

Main Views

• Game Theory (GT) is the study of strategic decision-making, where players' decisions affect each other. It includes two main branches: Non-Cooperative Game Theory (NCGT) and Cooperative Game Theory (CGT).

• CGT assumes that players can form binding agreements and that the focus is on the outcomes of cooperation, not the process of coalition formation. It often considers the Grand Coalition, which includes all players, as the most relevant for solution concepts.

• The Nash solution and the Kalai-Smorodinski solution are two of the most important bargaining solutions in CGT. The Nash solution is based on five axioms: individual rationality, Pareto optimality, independence from irrelevant alternatives, covariance under positive affine transformations, and symmetry. The Kalai-Smorodinski solution replaces the independence axiom with individual monotonicity, leading to a different but also unique solution.

• TU-games (Transferable Utility games) are games where the utility can be transferred among players, and the characteristic function is superadditive or convex. These properties are important in ensuring that cooperation is beneficial and that the grand coalition is efficient.

• The Core is a key subset solution concept, representing a set of allocations where no coalition has an incentive to deviate. If the Core is non-empty, it provides a range of equitable and efficient allocations. However, the Core can be empty, which indicates that there is no stable allocation that satisfies all coalitions' rationality.

• Other subset solution concepts include the bargaining set, kernel, least core, and stable sets, which provide alternative ways to evaluate the stability and fairness of allocations.

• Unique solution concepts include the Nucleolus and the Shapley value, which provide a single allocation that satisfies certain fairness and efficiency criteria. The τ-value is another unique solution that is particularly useful in cost allocation problems.

Key Information

• The paper is part of a larger study on cooperative arrangements for water allocation, funded by the Italian Trust Fund and the World Bank.

• It reviews existing literature on the use of CGT in environmental and water resource management, highlighting the importance of equity and fairness in the allocation of benefits or costs.

• The main models discussed are:

  • Bargaining games
  • Transferable Utility (TU) games
  • Non-Transferable Utility (NTU) games

• The paper also introduces cost-sharing rules, such as the Alternate Cost Avoided (ACA) and the Separable Cost Remaining Benefits (SCRB), which are used to allocate costs in cooperative settings.

• Superadditivity is a key property in TU-games, ensuring that the total gain from cooperation is at least the sum of individual gains. However, this assumption may not always hold in environmental applications due to externalities.

• Efficiency and individual rationality are fundamental in CGT, with the Core being a subset of efficient and individually rational allocations.

• The paper concludes that while CGT provides useful tools for understanding cooperation in resource allocation, it is important to consider the context-specific nature of equity and fairness, as well as the limitations of axiomatic approaches.

Structure of the Paper

• Introduction to Game Theory and Cooperative Game Theory
• Bargaining problems and their solutions (Nash and Kalai-Smorodinski)
• N-person cooperative games and the concept of characteristic functions
• Subset solution concepts (Core, bargaining set, kernel, least core, etc.)
• Unique solution concepts (Nucleolus, Shapley value, τ-value)
• Cost games and cost-sharing rules
• Concluding remarks on the use of CGT in environmental and water resource contexts

Conclusion

The paper provides a self-contained overview of CGT and its application to environmental and water resource issues, focusing on solution concepts that help in allocating gains and costs among players in a fair and efficient manner. It highlights the importance of equity, efficiency, and stability in cooperative settings and suggests that these concepts are crucial for policy-making and resource management.