Power asymmetry in conflict resolution with application to a water pollution dispute in China

© 2015. American Geophysical Union. All Rights Reserved. This is the peer reviewed version of the following article:Yu, J., Kilgour, D. M., Hipel, K. W., & Zhao, M. (2015). Power asymmetry in conflict resolution with application to a water pollution dispute in China. Water Resources Research, 51(10), 8627–8645, which has been published in final form at https://doi.org/10.1002/2014WR016257The concept of power asymmetry is incorporated into the framework of the Graph Model for Conflict Resolution (GMCR) and then applied to a water pollution dispute in China in order to show how it can provide strategic insights into courses of action. In a new definition of power asymmetry, one of the decision makers (DMs) in a conflict can influence the preferences of other DMs by taking advantage of additional options reflecting the particular DM's more powerful position. The more powerful DM may have three different kinds of power: direct positive, direct negative, or indirect. It is useful to analyze a model of a conflict without power asymmetry, and then to analyze a power-asymmetric model. As demonstrated by analysis of the water quality controversy that took place at the border separating the Chinese provinces of Jiangsu and Zhejiang, this novel conflict resolution methodology can be readily applied to real-world strategic conflicts to gain an enhanced understanding of the effects of asymmetric power.National Natural Science Foundation of China [71471087]Natural Sciences and Engineering Research Council of Canad

Energy Strategies for the Canadian Province of Ontario

The current and future energy situations in Canada are put into perspective, and the importance of nuclear energy and controversies surrounding it are investigated. More specifically, to demonstrate the important role nuclear energy has to play in Canada's future, a novel energy modeling tool, Canadian Energy Systems Simulator (CanESS), is employed. CanESS is a modeling platform with a huge database that assists an analyst in defining different energy scenarios by modifying the variables such as population and contributions of different energy sources to the overall production. The CanESS results clearly show that expansion of nuclear energy production is required to meet energy demand and simultaneously reduce greenhouse gas emissions. To formally study strategic issues connected to the ongoing conflict over nuclear power production in Ontario, the Graph Model for Conflict Resolution (GMCR) is utilized. This flexible systems methodology is used to study the nuclear disputes that existed in Ontario at two key points in time: the fall of 2008 and spring of 2010. The results of the 2008 analysis, especially the sensitivity analyses, show that the only decision makers (DMs) involved in the conflict who hold real power are the Federal and Ontario governments, although at the beginning of the investigation the Atomic Energy of Canada Ltd. (AECL) and the environmental groups had also been considered as participating DMs. The findings and information of the analysis in 2008, as well as an updated background for 2010, are used to perform another analysis in 2010. Meanwhile, their options or possible courses of action have also been changed. Again, at this stage the stable states of the game are found, and attitude analysis is carried out to obtain deeper insights about the dispute. The equilibria or potential resolutions of the 2008 analysis are found to be the transition states in the 2010 analysis. Specifically, it is discovered that if the Federal Government does have a negative attitude towards the Ontario Government, it is possible that the final outcome is a state that is among the least preferred states for both DMs. To formally study strategic issues connected to the ongoing conflict over nuclear power production in Ontario, the Graph Model for Conflict Resolution (GMCR) is utilized. This flexible systems methodology is used to study the nuclear disputes that existed in Ontario at two key points in time: the fall of 2008 and spring of 2010. The results of the 2008 analysis, especially the sensitivity analyses, show that the only decision makers (DMs) involved in the conflict who hold real power are the Federal and Ontario governments, although at the beginning of the investigation the Atomic Energy of Canada Ltd. (AECL) and the environmental groups had also been considered as participating DMs. The findings and information of the analysis in 2008, as well as an updated background for 2010, are used to perform another analysis in 2010. According to the results of the 2008 analysis, only the two governments are considered as the DMs in 2010. Meanwhile, their options or possible courses of action have also been changed. Again, at this stage the stable states of the game are found, and attitude analysis is carried out to obtain deeper insights about the dispute. The equilibria or potential resolutions of the 2008 analysis are found to be the transition states in the 2010 analysis. Specifically, it is discovered that if the Federal Government does have a negative attitude towards the Ontario Government, it is possible that the final outcome is a state that is among the least preferred states for both DMs

Studying Economic Sanctions Using The Graph Model for Conflict Resolution

The methodology of the Graph Model for Conflict Resolution (GMCR) is improved to show how a Graph Model can account for strength of sanctions, to introduce a trigger option to simplify a model, and to connect a Graph Model with the concept of BATNA (Best Alternative to Negotiated Agreement). Two real life applications are provided to illustrate these advances: the OPEC (Organization of Petroleum Exporting Countries)/US Shale oil producers conflict, and the North-South Sudan oil pipeline dispute. Sometimes disputants attempt to manipulate behavior by threatening sanctions. Clearly, the success of this threat depends on the strength of the sanctions. This type of conflict is represented in this thesis by two identical graphs with different preferences reflecting the strength of the sanction. Both of the real world conflicts examples are analyzed in this way. The concept of a Conflict Trigger (CT) is introduced to simplify a Graph Model. If the CT is selected, the number of states in the model can be significantly reduced, thereby, simplifying the analysis. The North/South Sudan conflict illustrates the employment of a CT for reducing the complexity of the analysis. BATNA is a widely utilized principle used in the analysis of negotiations. Because many negotiations can be captured in a Graph Model, it is reasonable to ask how BATNA is connected. The four steps of BATNA are compared to a typical Graph Model of a negotiation to identify similarities and differences. The use of BATNA’s reservation value in combination with a Graph Model of a negotiation gives insight into when a negotiator would accept an offer. The application of BATNA in the North/South Sudan conflict demonstrates its value

Initial State Stabilities and Inverse Engineering in Conflict Resolution

Two original contributions are made which extend the Graph Model for Conflict Resolution: one is a new family of solution concepts, while the other is a novel methodological approach. In addition to theoretical contributions, applications to complex energy problems are demonstrated; in particular, the consideration of the ongoing Trans Mountain Expansion Project is the first of its kind. The family of solution concepts, called initial state stabilities, is designed to complement existing solution concepts within the Graph Model framework by modelling both risk-averse and risk-seeking decision-makers. The comparison which underpins these concepts examines the consequences of moving from a given starting state to those of remaining in that state. The types of individuals modelled by these stability concepts represent a new class of decision-makers which, up until now, had not been considered in the Graph Model paradigm. The innovative methodology presented is designed to "inverse engineer" decision-makers’ preferences based on their observable behaviour. The algorithms underlying the inverse engineering methodology are based on the most commonly used stability concepts in the Graph Model for Conflict Resolution and function by reducing the set of possible preference rankings for each decision-maker. The reduction is based on observable moves and counter-moves made by decision-makers. This procedure assists stakeholders in optimizing their own decision-making process based on information gathered about their opponents and can also be used to improve the modelling of strategic interactions. In addition to providing decision-makers and analysts with up-to-date preference information about opponents, the methodology is also equipped with an ADVICE function which enriches the decision-making process by providing important information regarding potential moves. Decision-makers who use the methods introduced in this thesis are provided with the expected value of each of their possible moves, with the probability of the opponent’s next response, and with the opponent reachable states. This insightful data helps establish an accurate picture of the conflict situation and in so doing, aids stakeholders in making strategic decisions. The applicability of this methodology is demonstrated through the study of the conflict surrounding the Trans Mountain Expansion Project in British Columbia, Canada

Conflicting Attitudes in Environmental Management and Brownfield Redevelopment

An enhanced attitudes methodology within the framework of the Graph Model for Conflict Resolution (GMCR) is developed and applied to a range of environmental disputes, including a sustainable development conflict, an international climate change negotiation and a selection of brownfield conflicts over a proposed transfer of ownership. GMCR and the attitudes framework are first defined and then applied to a possible Sino-American climate negotiation over reductions in greenhouse gas emissions. A formal relationship between the attitudes framework and relative preferences is defined and associated mathematical theorems, which relate the moves and solution concepts used in both types of analysis, are proven. Significant extensions of the attitudes methodology are devised in the thesis. The first, dominating attitudes is a methodology by which the importance of a decision maker’s (DM’s) attitudes can be used to evaluate the strength of a given state stability. The second, COalitions and ATtitudes (COAT), is an expansion of both the attitudes and coalitions frameworks which allows one to analyze the impact of attitudes within a collaborative decision making setting. Finally, the matrix form of attitudes, is a mathematical methodology which allows complicated solution concepts to be executed using matrix operations and thus make attitudes more adaptable to a coding environment. When applied to environmental management conflicts, these innovative expansions of the attitudes framework illustrate the importance of cooperation and diplomacy in environmental conflict resolution

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