WPS4072

# **COOPERATIVE GAME THEORY AND ITS APPLICATION TO NATURAL, ENVIRONMENTAL AND WATER RESOURCE ISSUES:**

# **1. Basic Theory**

Irene Parrachino, Stefano Zara and Fioravante Patrone

## **Abstract**

Game theory provides useful insights into the way parties that share a scarce resource may plan their utilization of the resource under different situations. This review provides a brief and self-contained introduction to the theory of cooperative games. It can be used to get acquainted with the basics of cooperative games. Its goal is also to provide a basic introduction to this theory, in connection with a couple of surveys that analyze its use in the context of environmental problems and models. The main models (bargaining games, transfer utility and non transfer utility games) and issues and solutions are considered: bargaining solutions, single-value solutions like the Shapley value and the nucleolus, and multi-value solutions such as the core. The cooperative game theory (CGT) models that are reviewed in this paper favor solutions that include all possible players and ignore the strategic stages leading to coalition building. They focus on the possible results of the cooperation by answering questions such as: Which coalitions can be formed? And how can the coalitional gains be divided in order to secure a sustainable agreement? An important aspect associated with the solution concepts of CGT is the _equitable and fair_ sharing of the cooperation gains.

World Bank Policy Research Working Paper 4072, November 2006 _The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the view of the World Bank, its Executive Directors, or the countries they represent. Policy Research Working Papers are available online at http://econ.worldbank.org._ This Working paper is a product of the first phase of the study “Cooperative Arrangements for Allocation of Water among Production and Environmental Uses under Stochastic Supply Conditions”, funded by the Italian Trust Fund and the Development Economics Research Group of the World Bank. Members of the study team include: Ariel Dinar (Task Manager), Fioravante Patrone, Irene Parrachino, Stefano Zara of the University of Genoa, Carlo Carraro, Carmen Marchiori, and Alessandra Sgobbi of the University of Venice. Comments by Rashid Sumaila, University of British Columbia, Canada and Kim Hang Pham Do, Massey University, New Zealand, and participants of the 6<sup>th</sup> meeting on Game Theory and Practice Dedicated to Development, Natural Resources and the Environment, July 10-12, Zaragoza, Spain, are much appreciated. Two additional Working Papers are also devoted to some special topics, which are chosen having in mind their use in applications to environmental issues: 2. Application to Natural and Environmental Resources (PRWP 4073), and 3. Application to Water Resources (PRWP 4074).