Matrix Representations and Extension of the Graph Model for Conflict Resolution

The graph model for conflict resolution (GMCR) provides a convenient and effective means to model and analyze a strategic conflict. Standard practice is to carry out a stability analysis of a graph model, and then to follow up with a post-stability analysis, two critical components of which are status quo analysis and coalition analysis. In stability analysis, an equilibrium is a state that is stable for all decision makers (DMs) under appropriate stability definitions or solution concepts. Status quo analysis aims to determine whether a particular equilibrium is reachable from a status quo (or an initial state) and, if so, how to reach it. A coalition is any subset of a set of DMs. The coalition stability analysis within the graph model is focused on the status quo states that are equilibria and assesses whether states that are stable from individual viewpoints may be unstable for coalitions. Stability analysis began within a simple preference structure which includes a relative preference relationship and an indifference relation. Subsequently, preference uncertainty and strength of preference were introduced into GMCR but not formally integrated. In this thesis, two new preference frameworks, hybrid preference and multiple-level preference, and an integrated algebraic approach are developed for GMCR. Hybrid preference extends existing preference structures to combine preference uncertainty and strength of preference into GMCR. A multiple-level preference framework expands GMCR to handle a more general and flexible structure than any existing system representing strength of preference. An integrated algebraic approach reveals a link among traditional stability analysis, status quo analysis, and coalition stability analysis by using matrix representation of the graph model for conflict resolution. To integrate the three existing preference structures into a hybrid system, a new preference framework is proposed for graph models using a quadruple relation to express strong or mild preference of one state or scenario over another, equal preference, and an uncertain preference. In addition, a multiple-level preference framework is introduced into the graph model methodology to handle multiple-level preference information, which lies between relative and cardinal preferences in information content. The existing structure with strength of preference takes into account that if a state is stable, it may be either strongly stable or weakly stable in the context of three levels of strength. However, the three-level structure is limited in its ability to depict the intensity of relative preference. In this research, four basic solution concepts consisting of Nash stability, general metarationality, symmetric metarationality, and sequential stability, are defined at each level of preference for the graph model with the extended multiple-level preference. The development of the two new preference frameworks expands the realm of applicability of the graph model and provides new insights into strategic conflicts so that more practical and complicated problems can be analyzed at greater depth. Because a graph model of a conflict consists of several interrelated graphs, it is natural to ask whether well-known results of Algebraic Graph Theory can help analyze a graph model. Analysis of a graph model involves searching paths in a graph but an important restriction of a graph model is that no DM can move twice in succession along any path. (If a DM can move consecutively, then this DM's graph is effectively transitive. Prohibiting consecutive moves thus allows for graph models with intransitive graphs, which are sometimes useful in practice.) Therefore, a graph model must be treated as an edge-weighted, colored multidigraph in which each arc represents a legal unilateral move and distinct colors refer to different DMs. The weight of an arc could represent some preference attribute. Tracing the evolution of a conflict in status quo analysis is converted to searching all colored paths from a status quo to a particular outcome in an edge-weighted, colored multidigraph. Generally, an adjacency matrix can determine a simple digraph and all state-by-state paths between any two vertices. However, if a graph model contains multiple arcs between the same two states controlled by different DMs, the adjacency matrix would be unable to track all aspects of conflict evolution from the status quo. To bridge the gap, a conversion function using the matrix representation is designed to transform the original problem of searching edge-weighted, colored paths in a colored multidigraph to a standard problem of finding paths in a simple digraph with no color constraints. As well, several unexpected and useful links among status quo analysis, stability analysis, and coalition analysis are revealed using the conversion function. The key input of stability analysis is the reachable list of a DM, or a coalition, by a legal move (in one step) or by a legal sequence of unilateral moves, from a status quo in 2-DM or $n$-DM ($n > 2$) models. A weighted reachability matrix for a DM or a coalition along weighted colored paths is designed to construct the reachable list using the aforementioned conversion function. The weight of each edge in a graph model is defined according to the preference structure, for example, simple preference, preference with uncertainty, or preference with strength. Furthermore, a graph model and the four basic graph model solution concepts are formulated explicitly using the weighted reachability matrix for the three preference structures. The explicit matrix representation for conflict resolution (MRCR) that facilitates stability calculations in both 2-DM and $n$-DM ($n > 2$) models for three existing preference structures. In addition, the weighted reachability matrix by a coalition is used to produce matrix representation of coalition stabilities in multiple-decision-maker conflicts for the three preference frameworks. Previously, solution concepts in the graph model were traditionally defined logically, in terms of the underlying graphs and preference relations. When status quo analysis algorithms were developed, this line of thinking was retained and pseudo-codes were developed following a similar logical structure. However, as was noted in the development of the decision support system (DSS) GMCR II, the nature of logical representations makes coding difficult. The DSS GMCR II, is available for basic stability analysis and status quo analysis within simple preference, but is difficult to modify or adapt to other preference structures. Compared with existing graphical or logical representation, matrix representation for conflict resolution (MRCR) is more effective and convenient for computer implementation and for adapting to new analysis techniques. Moreover, due to an inherent link between stability analysis and post-stability analysis presented, the proposed algebraic approach establishes an integrated paradigm of matrix representation for the graph model for conflict resolution

Status Quo Analysis of the Flathead River Conflict

Status quo analysis algorithms developed within the paradigm of the graph model for conflict resolution are applied to an international river basin conflict involving the United States and Canada to assess the likeliness of various compromise resolutions. The conflict arose because the state of Montana feared that further expansion of the Sage Creek Coal Company facilities in Canada would pollute the Flathead River, which flows from British Columbia into Montana. Significant insights not generally available from a static stability analysis are obtained about potential resolutions of the conflict under study and about how decision makers’ interactions may direct the conflict to distinct resolutions. Analyses also show how political considerations may affect a particular decision maker’s choice, thereby influencing the evolution of the conflict

Applications of negotiation theory to water issues

The authors review the applications of noncooperative bargaining theory to waterrelated issues-which fall in the category of formal models of negotiation. They aim to identify the conditions under which agreements are likely to emerge and their characteristics, to support policymakers in devising the"rules of the game"that could help obtain a desired result. Despite the fact that allocation of natural resources, especially trans-boundary allocation, has all the characteristics of a negotiation problem, there are not many applications of formal negotiation theory to the issue. Therefore, the authors first discuss the noncooperative bargaining models applied to water allocation problems found in the literature. Key findings include the important role noncooperative negotiations can play in cases where binding agreements cannot be signed; the value added of politically and socially acceptable compromises; and the need for a negotiated model that considers incomplete information over the negotiated resource.Water Supply and Sanitation Governance and Institutions,Town Water Supply and Sanitation,Water and Industry,Environmental Economics&Policies,Water Conservation

Applications of negotiation theory to water issues

The purpose of the paper is to review the applications of non-cooperative bargaining theory to water related issues – which fall in the category of formal models of negotiation. The ultimate aim is that of, on the one hand, identify the conditions under which agreements are likely to emerge, and their characteristics; and, on the other hand, to support policy makers in devising the “rules of the game” that could help obtain a desired result. Despite the fact that allocation of natural resources, especially of trans-boundary nature, has all the characteristics of a negotiation problem, there are not many applications of formal negotiation theory to the issue. Therefore, this paper first discusses the noncooperative bargaining models applied to water allocation problems found in the literature. Particular attention will be given to those directly modelling the process of negotiation, although some attempts at finding strategies to maintain the efficient allocation solution will also be illustrated. In addition, this paper will focus on Negotiation Support Systems (NSS), developed to support the process of negotiation. This field of research is still relatively new, however, and NSS have not yet found much use in real life negotiation. The paper will conclude by highlighting the key remaining gaps in the literature.Negotiation theory, Bragaining, Coalitions, Fairness, Agreements

Risk Aversion in International Relations Theory

|When international relations theorists use the concept of risk aversion, they usually cite the economics conception involving concave utility functions. However, concavity is meaningful only when the goal is measurable on an interval scale. International decisions are usually not of this type, so that many statements appearing in the literature are formally meaningless. Applications of prospect theory face this difficulty especially, as risk aversion and acceptance are at their center. This paper gives two definitions of risk attitude that do not require an interval scale. The second and more distinctive one uses the property of submodularity in place of concavity. R. D. Luce has devised a theory of choice with features of prospect theory but not requiring on an interval scale, and the second definition in combination with this theory yields the traditional claim that decision makers are risk-averse for gains and risk-seeking for losses.risk aversion, prospect theory, international relations, joint receipts, measurement theory.

State-of-the-Art Report on Systems Analysis Methods for Resolution of Conflicts in Water Resources Management

Water is an important factor in conflicts among stakeholders at the local, regional, and even international level. Water conflicts have taken many forms, but they almost always arise from the fact that the freshwater resources of the world are not partitioned to match the political borders, nor are they evenly distributed in space and time. Two or more countries share the watersheds of 261 major rivers and nearly half of the land area of the wo rld is in international river basins. Water has been used as a military and political goal. Water has been a weapon of war. Water systems have been targets during the war. A role of systems approach has been investigated in this report as an approach for resolution of conflicts over water. A review of systems approach provides some basic knowledge of tools and techniques as they apply to water management and conflict resolution. Report provides a classification and description of water conflicts by addressing issues of scale, integrated water management and the role of stakeholders. Four large-scale examples are selected to illustrate the application of systems approach to water conflicts: (a) hydropower development in Canada; (b) multipurpose use of Danube river in Europe; (c) international water conflict between USA and Canada; and (d) Aral See in Asia. Water conflict resolution process involves various sources of uncertainty. One section of the report provides some examples of systems tools that can be used to address objective and subjective uncertainties with special emphasis on the utility of the fuzzy set theory. Systems analysis is known to be driven by the development of computer technology. Last section of the report provides one view of the future and systems tools that will be used for water resources management. Role of the virtual databases, computer and communication networks is investigated in the context of water conflicts and their resolution.https://ir.lib.uwo.ca/wrrr/1005/thumbnail.jp

Network Analysis, Creative System Modelling and Decision Support: The NetSyMoD Approach

This paper presents the NetSyMoD approach – where NetSyMod stands for Network Analysis – Creative System Modelling – Decision Support. It represents the outcome of several years of research at FEEM in the field of natural resources management, environmental evaluation and decision-making, within the Natural Resources Management Research Programme. NetSyMoD is a flexible and comprehensive methodological framework, which uses a suite of support tools, aimed at facilitating the involvement of stakeholders or experts in decision-making processes. The main phases envisaged for the process are: (i) the identification of relevant actors, (ii) the analysis of social networks, (iii) the creative system modelling and modelling of the reality being considered (i.e. the local socio-economic and environmental system), and (iv) the analysis of alternative options available for the management of the specific case (e.g. alternative projects, plans, strategies). The strategies for participation are necessarily context-dependent, and thus not all the NetSyMod phases may be needed in every application. Furthermore, the practical solutions for their implementation may significantly differ from one case to another, depending not only on the context, but also on the available resources (human and financial). The various applications of NetSyMoD have nonetheless in common the same approach for problem analysis and communication within a group of actors, based upon the use of creative thinking techniques, the formalisation of human-environment relationships through the DPSIR framework, and the use of multi-criteria analysis through the mDSS software.Social Network, Integrated Analysis, Participatory Modelling, Decision Support

An integrated multiple criteria preference ranking approach to the Canadian west coast port congestion conflict

An integrative conflict analysis approach, incorporating an Analytic Hierarchy Process (AHP) based preference ranking method into the Graph Model for Conflict Resolution (GMCR), is employed to investigate the Canadian west coast port congestion dispute. The Canadian west coast has historically been an important gateway connecting North America to Asia thanks to its specific geographical and strategic location. Despite successful operations and maintenance of the port facilities to handle international trade during the past few decades, the west coast is now facing increasing congestion problems, resulting in significant delays in transporting goods from the west coast to other parts of Canada and the USA. The strategic analyses carried out in this research suggest potential resolutions in which Canada would expand port facilities at various locations, encouraging traders to continue choosing the Canadian west coast as one of their trade gateways to North America

Status quo analysis of the Flathead River conflict. Water Resources Research

Status quo analysis algorithms developed within the paradigm of the graph model for conflict resolution are applied to an international river basin conflict involving the United States and Canada to assess the likeliness of various compromise resolutions. The conflict arose because the state of Montana feared that further expansion of the Sage Creek Coal Company facilities in Canada would pollute the Flathead River, which flows from British Columbia to Montana. Significant insights not generally available from a static stability analysis are obtained about potential resolutions of the conflict under study and about how decision makers’ interactions may direct the conflict to distinct resolutions. Analyses also show how political considerations may affect a particular decision maker’s choice, thereby influencing the evolution of the conflict