Keith W. Hipel

Solving Complex Conflicts

Many complex problems may be modeled as conflicts, but until now a comprehensive technique for analyzing real world conflicts has not been available. A method is presented which permits the rapid assessment of complex conflict situations for the purpose of finding resolutions to a conflict, determining correct strategies, and enhancing ones understanding of the problem. The new technique is presented through a step by step example, and following this the mathematical basis for the analysis algorithm is developed. Finally, extensions to the procedure are presented through the analysis of the fall of France in 1940, an international water allocation conflict, and the Garrison Diversion Unit (GDU) irrigation project in North Dakota, U.S.A.

The graph model for conflicts

The graph model for conflicts is developed as a comprehensive methodology for realistically analyzing real world conflicts. The graph form takes outcomes, rather than individual decisions, as the basic units for describing a conflict. In the graph form, many solution concepts can be formulated for both two-player and multiplayer games. In particular, specific mathematical criteria are presented for categorizing solution concepts which can be used for predicting equilibria in n-player games. One of the criteria on which this taxonomy of solution concepts is based is the number of steps ahead a player may think, in terms of the reactions of other players to his actions. Other criteria include which players take part in the sanctioning process, and whether sanctioning moves are restricted to those which lead to immediate improvements for the mover. In order to demonstrate the insight which decision makers can gain from studying a dispute using the graph model, various solution concepts are applied to an important environmental engineering problem.

A decision support system for interactive decision making-Part I: model formulation

A comprehensive decision support system, GMCR II, is developed for the systematic study of real-world interactive decision problems. Model formulation is presented in Part I, and analysis and output interpretation in Part II. GMCR II is based upon existing and new research developments of the graph model for conflict resolution. In Part I, specially designed data structures and corresponding algorithms are implemented for generating and representing possible states, removing infeasible states, coalescing indistinguishable states, and specifying and storing allowable state transitions. Algorithms implementing different approaches to the elicitation of preferences over states enable GMCR II to construct and manage an efficient, flexible, and complete graph model of a strategic conflict.

The decision support system GMCR in environment conflict management

The graph model for conflict resolution is put forward as a unique decision technology for systematically studying strategic conflicts that can arise in environmental management and elsewhere. This flexible conflict resolution methodology has solid and realistic mathematical foundations which permit it to model strategic decisions accurately, forecast compromise solutions, and assist in assessing the political, economic, environmental, and social viability of alternative scenarios to resolving environmental conflicts. To permit practitioners to conveniently apply the graph model for conflict resolution to practical real-world conflict problems, a new decision support system called GMCR II (Graph Model for Conflict Resolution II) is designed. To explain the basic structure of GMCR II and how it works in practice, this paper describes its use to model and analyze an international environmental management dispute that took place in North America.

A decision support system for interactive decision making - Part II: analysis and output interpretation

For pt.I see ibid., p.42-55 (2003). The development of a comprehensive decision support system, GMCR II, for the systematic study of real-world interactive decision problems is presented. The companion paper (Part I), discusses how GMCR II elicits, stores, and manages conflict models; here (Part II), the focus is on GMCR IIs analysis and output interpretation subsystems. Specifically, this paper describes the powerful and efficient analysis engine contained in GMCR II, its informative output presentation and interpretation facilities, and a number of follow-up analyses. Furthermore, an illustrative case study is used to demonstrate how GMCR II can be conveniently applied in practice.

Preference uncertainty in the graph model for conflict resolution

A new preference structure is introduced into the graph model for conflict resolution. This structure can handle a decision-makers (DM) strict preference for one state or scenario over another, equal preference for states, and uncertain or unknown preference in the comparison of two states. Built upon this preference structure, four types of solution definitions modeling human behavior under conflict are extended to accommodate uncertainty in preferences. Four distinct ways to consider uncertain preference information are identified, producing sixteen extended stability definitions. Interrelationships of these definitions within and across the four definition sets are investigated. Illustrative examples of two-DM and multi-DM conflict models are presented to show how the new solution concepts can be applied in practice.

Coalition Analysis in Group Decision Support

GMCR II, a decision support system based on the Graph Model for Conflict Resolution, now contains an algorithm for Coalition Analysis to alert users that certain decision-makers would find it both feasible and beneficial to co-ordinate their actions. The theory and implementation of Coalition Analysis in GMCR II are discussed and illustrated.

Basin-wide cooperative water resources allocation

The Cooperative Water Allocation Model (CWAM) is designed within a general mathematical programming framework for modeling equitable and efficient water allocation among competing users at the basin level and applied to a large-scale water allocation problem in the South Saskatchewan River Basin located in southern Alberta, Canada. This comprehensive model consists of two main steps: initial water rights allocation and subsequent water and net benefits reallocation. Two mathematical programming approaches, called the priority-based maximal multiperiod network flow (PMMNF) method and the lexicographic minimax water shortage ratios (LMWSR) technique, are developed for use in the first step. Cooperative game theoretic approaches are utilized to investigate how the net benefits can be fairly reallocated to achieve optimal economic reallocation of water resources in the second step. The application of this methodology to the South Saskatchewan River Basin shows that CWAM can be utilized as a tool for promoting the understanding and cooperation of water users to achieve maximum welfare in a river basin and minimize the potential damage caused by water shortages, through water rights allocation, and water and net benefit transfers among water users under a regulated water market or administrative allocation mechanism.

Strength of Preference in the Graph Model for Conflict Resolution

A new preference structure that includes a simple relative measure of strength of preference is developed and integrated into some of the stability definitions for the graph model for conflict resolution. In this triplet preference structure, a decision-maker may greatly prefer or prefer one state or scenario to another, or may be indifferent between them. Four stability definitions (solution concepts), Nash stability (R), general metarationality (GMR), symmetric metarationality (SMR), and sequential stability (SEQ), are extended to include strong and weak stabilities for the case of conflicts with two decision makers. Theorems that clarify the interrelationships of the strong and weak versions of these solution concepts are presented. The application of this new preference structure and the associated solution concepts is demonstrated in an environmental conflict model, called the Sustainable Development Conflict. This case shows that valuable strategic insights are gained when strength of preference is integrated into the stability analysis.

Forecasting monthly riverflow time series

Abstract Mean monthly flows from thirty rivers in North and South America are used to test the short-term forecasting ability of seasonal ARIMA, deseasonalized ARMA, and periodic autoregressive models. The series were split into two sections and models were calibrated to the first portion of the data. The models were then used to generate one-step-ahead forecasts for the second portion of the data. The forecast performance is compared using various measures of accuracy. The results suggest that a periodic autoregressive model, identified by using the partial autocorrelation function, provided the most accurate forecasts