Probabilistic Preferences in the Graph Model for Conflict Resolution

Conflict of environmental sustainable development as a common phenomenon can be seen everywhere in life. To capture consensus problems of decision makers (DMs) in conflict, a consensus and non-consensus fuzzy preference relation (FPR) matrix is proposed to the framework of the Graph Model for Conflict Resolution (GMCR). Concentrating on the case of two DMs within GMCR paradigm, four standard fuzzy solution concepts are developed into eight fuzzy stability definitions which can fully represent DMs’ behavior characteristics of win-win and self-interested. To demonstrate how the novel GMCR methodology proposed in this paper can be conveniently utilized in practice, it is then applied to an environmental sustainable development conflict with two DMs. The results show that the general fuzzy equilibrium solutions are the intersection of consensus fuzzy equilibrium and non-consensus fuzzy equilibrium. Therefore, the GMCR technique considering DMs’ consensus can effectively predict the various possible solutions of conflict development under different DMs’ behavior preferences and provide new insights for analysts into a conflict.

Many solution concepts have been proposed within the Graph Model for Conflict Resolution to represent many behaviors that decision makers (DMs) can have in strategic settings. Among these solution concepts, the limited move stability stands out because it allows analyzing the conflict a variable number of steps forward, taking into account the preferences of all DMs involved in the conflict. However, for conflicts involving more than two DMs, there are two definitions of limited move stability that we argue to have undesired properties. For that reason, we present two alternative definitions for limited move stability for conflicts with multiple DMs, called: Alternative Limited-Move stability with Cooperative Coalition ( $$L_h^{CC}$$ ) and Alternative Limited-Move stability with Individualistic Coalition ( $$L_h^{CI}$$ ). Moreover, we obtained results relating these concepts to classical GMCR stability concepts. Furthermore, we provide results that establish the equivalence among the stability notions $$L_h^{CC}$$ , $$L_h^{CI}$$ and $$\text {Maximin}_h$$ , for conflicts in which the DMs belonging to the opposing coalition have equal and completely opposite preferences to those of the focal DM. An application to the Elmira conflict illustrates the usefulness of the proposed concepts in a real conflict situation.

This paper proposes a new algebraic definition that facilities calculating of Stackelberg stability in a graph model for conflict resolution with two decision makers. Most stability definitions used in the graph model methodology place decision makers at the same level, in the sense that their roles are symmetric. In practice, however, one decision maker may join by forcing the other to respond to his or her decision. So, to be applied, a model must specify the leader and the follower. Stackelberg stability can be defined logically, but an algorithm to implement it has not been developed until now, due to its complicated recursive formula. To permit Stackelberg stability to be calculated efficiently and encoded conveniently, within a decision support system, an algebraic test for the stability is developed. This algebraic representation of Stackelberg stability is easy to implement and interpret. A superpower military confrontation is used to illustrate how Stackelberg stability can be employed to a real-world application using the new approach.KeywordsConflict analysisDecision makerAlgebraic expressionsStackelberg stabilityGraph modelOrdinal preferences

A hybrid preference framework is proposed for strategic conflict analysis to integrate preference strength and preference uncertainty into the paradigm of the graph model for conflict resolution (GMCR) under multiple decision makers. This structure offers decision makers a more flexible mechanism for preference expression, which can include strong or mild preference of one state or scenario over another, as well as equal preference. In addition, preference between two states can be uncertain. The result is a preference framework that is more general than existing models which consider preference strength and preference uncertainty separately. Within the hybrid preference structure, four kinds of stability are defined as solution concepts and a post-stability analysis, called status quo analysis, which can be used to track the evolution of a given conflict. Algorithms are provided for implementing the key inputs of stability analysis and status quo analysis within the extended preference structure. The new stability concepts under the hybrid preference structure can be used to model complex strategic conflicts arising in practical applications, and can provide new insights for the conflicts. The method is illustrated using the conflict over proposed bulk water exports from Lake Gisborne in Newfoundland, Canada.

Conflict is an inevitable social phenomenon and the analysis of it can effectively resolve disputes, improve the position of decision makers (DMs), forecast compromise solutions as well. At present, the Graph Model for Conflict Resolution (GMCR), a completely non-quantitative decision support system (DSS) based on DM’s ordinal preference information, is constructed to combat conflict analysis complicated by multiple participant or multiple criteria or both. The purpose of the study is to introduce an overview of GMCR in conflict analyzing through bibliometrics. In order to achieve this goal, a systematic review of articles in leading journals of Web of Science Core Collection (WoSCC) during 1987–2019 is posed, referring to the distribution of countries, institutions, authors, subjects and journals, research topics and hotspots exploration as well as frontiers prediction, by utilizing VOSviewer and CiteSpace. The contributions of this study are not only providing a handy method to grasp generalized scientific research situation, but also demonstrating status quo and emerging trends of GMCR for researchers and everyone who interested in.

A new analysis technique, appropriate to situations of high preference uncertainty, is added to the graph model for conflict resolution methodology. Interval fuzzy stabilities are now formulated, based on decision makers’ (DMs’) interval fuzzy preferences over feasible scenarios or states in a conflict. Interval fuzzy stability notions enhance the applicability of the graph model, and generalize its crisp and fuzzy preference-based stability ideas. A graph model is both a formal representation and an analysis procedure for multiple participant-multiple objective decisions that employs stability concepts representing various forms of human behavior under conflict. Defined based on a type-2 fuzzy logic, an interval fuzzy preference for one state over another is represented by a subinterval of [0, 1] indicating an interval-valued preference degree for the first state over the second. The interval fuzzy stabilities put forward in this research are interval fuzzy Nash stability, interval fuzzy general metarational stability, interval fuzzy symmetric metarational stability, and interval fuzzy sequential stability. A state is interval fuzzy stable for a DM if moving to any other state is not adequately desirable to the DM; where adequacy is measured by the interval fuzzy satisficing threshold of the DM and farsightedness, involving possible moves and countermoves by DMs, is determined by the interval fuzzy stability notion selected. Note that infinitely many degrees in an interval-valued preference are preserved in characterizing the desirability of a move. A state from which no DM can move to any sufficiently desirable scenario is an interval fuzzy equilibrium, and is interpreted as a possible resolution of the strategic conflict under study. The new stability concept is illustrated through its application to an environmental conflict that took place in Elmira, Ontario, Canada. Insightful results are identified and discussed.

The graph model for conflict resolution (GMCR), along with its associated decision support system GMCR II, is employed for systematically studying the strategic aspects of a conflict existing in Per Aru basin. National Water Supply & Drainage Board has planned to build a reservoir on the Per Aru for the sole purpose of supplying drinking water to the urban areas of Vavuniya district. People who will be affected due to the inundation of their lands have shown resistance to the construction of the reservoir. Moreover, government organizations such as Forest Department and Wildlife Department also have expressed their concerns over the construction of a reservoir since that will have diverse impacts on forest lands and wildlife in the area that will be inundated by the proposed reservoir. The above three stakeholders, viz., National Water Supply & Drainage Board, affected people and government organizations suggest a few options to solve the conflict.The options are specific actions that can actually occur in a conflict. The decision support system, GMCR II, was used to investigate and resolve this conflict. The paper presents all the steps involved in the modeling of the conflict using GMCR II and analysis of the results obtained from the model. The National Water Supply & Drainage Board accepting to reduce the inundation area and agreeing to release sufficient environmental flow was resulted as the best possible solution acceptable for all the three parties.The solution includes affected people and Government Organizations agreeing for the construction of the reservoir at the original location. ENGINEER, Vol. 47, No. 03, pp. 61-70, 2014

On some properties of limited move stability, generalized metarationality, and policy equilibrium in bilateral conflicts

To demonstrate the strategic influence a third party can have on negotiations, a formal approach to resolving a complex conflict is applied to an important international water resources controversy. Specifically, third party intervention is employed within the framework of the Graph Model for Conflict Resolution (GMCR) to systematically investigate the ongoing dispute between Bangladesh and India over the regulation of the Ganges River by India at the Farakka Barrage located just upstream on the Ganges River in India before it flows into Bangladesh. A general system of systems engineering approach to Third Party Intervention within the GMCR structure is designed to reflect a range of ways in which it can be implemented in practice. Having an insightful and powerful tool like Third Party GMCR permits one to ascertain how a Third Party can guide a serious conflict to a more reasonable resolution which may be mutually beneficial to all concerned parties.

Conflict Analysis is a set of techniques to model and analyze a strategic conflict, or policy problem, using models of the purposive behavior of actors. After a review of these methods, the Graph Model for Conflict Resolution, which stands out for the flexibility of its models and the breadth of its analysis, is described in detail. After an historical overview, its development is compared to other Conflict Analysis techniques, including Drama Theory (See the chapter by Bryant, this volume), and to the Non-cooperative Game Theory (Chatterjee, in this volume) that inspired them. The graph model system is prescriptive, aiming to provide a specific decision-maker with relevant and insightful strategic advice. The capacity of the graph model to generate useful advice is emphasized throughout, and illustrated using a real-life groundwater contamination dispute. The description of the graph model includes the basic modeling and analysis components of the methodology and the decision support system GMCR II that has been used to apply it, including both basic (stability) analysis and follow-up analysis. New developments ensure that the next generation of decision support based on the graph model will be much more comprehensive and powerful.

A novel approach for assessing the robustness of an equilibrium in conflict resolution is presented. Roughly, an equilibrium is robust if it is resilient, or resistant to deviation. Robustness assessment is based on a new concept called Level of Freedom, which evaluates the relative freedom of a decision maker to escape an equilibrium. Resolutions of a conflict can be affected by changes in decision makers’ preferences, which may destabilize an equilibrium, causing the conflict to evolve. Hence, a conflict may become long-term and thereby continue to evolve, even after reaching an equilibrium. The new robustness measure is used to rank equilibria based on robustness, to facilitate distinguishing equilibria that are relatively sustainable. An absolutely robust equilibrium is a special case in which the level of freedom is at an absolute minimum for each individual stability definition.

Third-party mediation has been proved to be an effective way to resolve conflicts. T he p reference optimization based on inverse Graph Model for Conflict Resolution (GMCR) provides strong theoretical support for the formulation of a third-party mediation scheme. Real-world conflict parties have complicated preferences, which may or may not be transferred. In order to determine an optimal preference under the desired equilibrium, this work considers the conditions of transitive preferences into the current preference optimization model based on inverse GMCR. Only non-transmitted preferences have been examined in the current inverse preference research. Due to its intuitiveness, Directed Acyclic Giagram (DAG) is utilized to express the transitive preference structure in order to more accurately represent preference. The desired preference is then searched for across a large number of preference profiles by using a Genetic Algorithm-based approach. Double genes are designed: permutation gene and connected gene make up the, which is successful to solve the problem. These two genes can be converted to decision-maker's (DM's) preference matrix by specific permutations a nd transformations. Finally, a case of water resource conflict i s used to verify 0 ur work's rationality and practical significance.

An option prioritization technique is developed to efficiently elicit the preferences, both unknown and crisp, of decision makers (DMs) in strategic conflicts. In the Graph Model for Conflict Resolution, each DM has one or more options, each of which may be selected or not. A state, or possible scenario, is formed when all DMs make an option selection. The software GMCR II contains an option prioritization procedure that makes it easy for a modeller to enter a DM’s crisp preference ordering over the states using prioritized statements describing the DM’s preferred option combinations. This procedure is extended by adding two new logical connectives that describe uncertainty of preference. For each DM, a range of possible scores for each feasible state can then be calculated, facilitating the determination of a preference ordering containing uncertainty by comparing and ranking scores. To demonstrate how this new methodology can be used to represent unknown preferences in a real-world decision problem, it is applied to a Canadian dispute over proposed water exports.

ABSTRACTTo capture decision-makers' (DMs') various kinds of misperceptions in a conflict setting, a methodology is developed to improve hypergame analysis within the framework of the graph model for conflict resolution. This technique models and analyses DMs' different levels of perception in a real-life situation. It also handles a DM's misperception about itself as well as misperception about its opponents. A hypergame in graph form is a framework that consists of subjective hypergames, each of which illustrates a given DM's viewpoint of the hypergame situation. The universal sets of options and states for the hypergame, which include all possible perceptual options and states for the conflict, are used to construct each DM's subjective hypergame. To gain worthy strategic insights from the hypergame analysis, the overall hypergame equilibria are classified based on the types of misperceptions and the awareness of DMs into eight classes of resolutions.

A novel two-level hierarchical graph model is developed to analyze international climate change negotiations with hierarchical structures: the negotiations take place between two nations and between each nation and its provincial governments. The two national government are two decision makers at the top level. Within each nation, the two provincial governments negotiate with the national government at the lower level. The theoretical structure of this novel model, including decision makers, options, moves, and preference relations, are developed. The interrelationship between the stabilities in the two-level hierarchical graph model and the stabilities in local models are investigated by theorems. These theorems can be utilized to calculate complete stabilities in the two-level hierarchical graph model when the stabilities in local graph models are known. The international climate change negotiations as the illustrative example is then investigated in detail. The extra equilibrium, uniquely obtained by this novel methodology, suggests that opposition may still be from one provincial government when the national government does not sign the international climate agreement and implements existing environmental laws. Compared with other approaches, this novel methodology is an effective and flexible tool in analyzing hierarchical conflicts at two levels by providing decision makers with strategic resolutions with broader vision.