A Maximin$$_h$$ Matrix Representation in the Graph Model for Conflict Resolution

The fundamental design and inherent capabilities of the Graph Model for Conflict Resolution (GMCR) to address a rich range of complex real world conflict situations are put into perspective by tracing its historical development over a period spanning more than thirty years, and highlighting great opportunities for meaningful future expansions within an era of artificial intelligence (AI) and intensifying conflict in an over-crowded world. By constructing a sound theoretical foundation for GMCR based upon assumptions reflecting what actually occurs in reality, a fascinating story is narrated on how GMCR was able to expand in bold new directions as well as take advantages of many important legacy decision technologies built within the earlier Metagame Analysis and later Conflict Analysis paradigms. From its predecessors, for instance, GMCR could take advantage of option form put forward within Metagame Analysis for effectively recording a conflict as well as preference elicitation techniques and solution concepts for defining chess-like behavior when calculating stability of states from the realm of Conflict Analysis. The key ideas outlined in the paper underlying the current and projected capabilities of GMCR include the development of four different ways to handle preference uncertainty in the presence of either transitive or intransitive preferences; a wide range of solution concepts for describing many kinds of human behavior under conflict; unique coalition analysis algorithms for determining if a given decision maker can fare better in a dispute via cooperation; tracing the evolution of a conflict over time; and the matrix formulation of GMCR for computational efficiency when calculating stability and also theoretically expanding GMCR in new directions. The basic design of a Decision Support System for permitting researchers and practitioners to readily apply the foregoing and other advancements in GMCR to tough real world controversies is discussed. Inverse engineering is mentioned as an AI extension of GMCR for computationally determining the preferences required by decision makers in order to reach a desirable state, such as a climate change agreement in which all nations significantly cut back on their greenhouse gas emissions. Although GMCR has been successfully applied to challenging disputes arising in many different fields, a simple climate change negotiation conflict between the US and China is utilized to explain clearly key concepts mentioned throughout the fascinating historical journey surrounding GMCR.

Matrix representation of stability definitions in the graph model for conflict resolution with grey-based preferences

A survey of the design, development and implementation of a flexible decision technology called the graph model for conflict resolution (GMCR) is discussed for systematically investigating real world conflicts within a system of systems engineering outlook. This encompassing GMCR methodology has been constructed during the past three decades by the authors, their colleagues and students from many countries for addressing a rich range of conflict situations. GMCR can be used for studying large and small conflicts and includes methods for preference elicitation, preference uncertainty (unknown, fuzzy, grey numbers and probabilistic). Many kinds of definitions exist for possible human behavior under pure competition which can be transformed for utilization in coalition analysis. GMCR can handle emotions, attitudes, and misperceptions. Within inverse GMCR, one can calculate the preferences needed by decision makers (DMs) to reach a desirable equilibrium. Under behavioral GMCR one can ascertain the strategic thinking of DMs when the input and output are known. Decision support systems can be built for implementing the array of GMCR advancements. Future expansions of GMCR can be guided by key characteristics of actual disputes. Artificial intelligence (AI) GMCR is a promising subfield of study within GMCR.

The fundamental design and inherent capabilities of the Graph Model for Conflict Resolution (GMCR) to address a rich range of complex real world conflict situations are put into perspective by tracing its historical development over a period spanning more than 30 years, and highlighting great opportunities for meaningful future expansions within an era of artificial intelligence (AI) and intensifying conflict in an over-crowded world. By constructing a sound theoretical foundation for GMCR based upon assumptions reflecting what actually occurs in reality, a fascinating story is narrated on how GMCR was able to expand in bold new directions as well as take advantage of many important legacy decision technologies built within the earlier Metagame Analysis and later Conflict Analysis paradigms. From its predecessors, for instance, GMCR could benefit by the employment of option form put forward within Metagame Analysis for effectively recording a conflict, as well as preference elicitation techniques and solution concepts for defining chess-like behavior when calculating stability of states from the realm of Conflict Analysis. The key ideas outlined in the paper underlying the current and projected capabilities of GMCR include the development of four different ways to handle preference uncertainty in the presence of either transitive or intransitive preferences; a wide range of solution concepts for describing many kinds of human behavior under conflict; unique coalition analysis algorithms for determining if a given decision maker can fare better in a dispute via cooperation; tracing the evolution of a conflict over time; and the matrix formulation of GMCR for computational efficiency when calculating stability and also theoretically expanding GMCR in bold new directions. Inverse engineering is mentioned as an AI extension of GMCR for computationally determining the preferences required by decision makers in order to reach a desirable state, such as a climate change agreement in which all nations significantly cut back on their greenhouse gas emissions. The basic design of a decision support system for permitting researchers and practitioners to readily apply the foregoing and other advancements in GMCR to tough real world controversies is discussed. Although GMCR has been successfully applied to challenging disputes arising in many different fields, a simple climate change negotiation conflict between the US and China is utilized to explain clearly key concepts mentioned throughout the fascinating historical journey surrounding GMCR.

Matrix representations of the inverse problem in the graph model for conflict resolution with fuzzy preference

Matrix representation of the graph model for conflict resolution based on intuitionistic preferences with applications to trans-regional water resource conflicts in the Lancang–Mekong River Basin

The Graph Model for Conflict Resolution is a flexible methodology for systematically studying strategic conflicts in the real world, and is therefore a natural tool for negotiation support. The basic definitions underlying the graph model are reviewed, and the techniques for analysis and interpretation are discussed. The modeling and analysis of a case study, an international trade negotiation concerning the export of Canadian softwood lumber to the United States, are used to demonstrate the practical application of the Graph Model for Conflict Resolution as a negotiation support tool. The modeling and analysis is carried out using the GMCR software system. The ability of the Graph Model for Conflict Resolution to provide insights and advice to negotiators is emphasized.

An encompassing methodology, the Graph Model for Conflict Resolution (GMCR), is applied to a controversial groundwater contamination dispute to demonstrate how to obtain valuable strategic insights that can lead to informed decisions. Because of GMCR’s inherently flexible systems design, both researchers and practitioners can utilize it to investigate conflict in any field. Appreciating the ability of GMCR to rigorously model and analyze actual conflict makes it easier to follow the mathematical developments in later chapters. This book contains many specific contributions, such as structures for representing preference and solution concepts describing human interactions under conflict. It describes both independent and cooperative behavior within GMCR, in both the logical and matrix formulations. A road map will help the reader navigate through these ideas and procedures. A new decision support system captures these recent GMCR developments to realize fully the capability of GMCR to address the broader scope of human strategic conflict. This chapter is essential reading as preparation for each of the other chapters in this book.

Mixed coalition analysis approaches are developed within the framework of the graph model for conflict resolution (GMCR) for analyzing the heterogeneous multicoalitional opponents having mixed coalitional sanctions, in which some sanctioning coalitions may only invoke coalitional improvements (CIs) while others may go to any reachable states to jointly sanction a focal coalition's CIs. To accomplish this, the concept of a full coalition set is defined in which each participating decision maker (DM) is represented once either as an individual player or part of a coalition. All possible scenarios in which a full coalition set could be formed is called the universal coalition set. When calculating the stability of a specific state for a particular coalition in a given conflict, the remaining DMs form the universal coalition set whose moves have the potential to block any CIs by the focal coalition within four specified solution concepts having full participation of sanctioning opponents. To handle heterogeneous opponents with mixed CIs (MCIs), the mixed coalition analysis approach is proposed, which provides a more general coalition analysis framework than existing coalition analysis approaches. Moreover, the interrelationships among coalitional stabilities and mixed coalitional stabilities with full participation are investigated followed by their corresponding matrix representations which can significantly improve their computational efficiency and make the computer implementation possible. Finally, a case study is investigated to demonstrate how to employ the proposed mixed coalition analysis approaches to address a real-world environmental conflict.

This study employs the Graph Model for Conflict Resolution (GMCR) to systematically analyze and evaluate potential solutions to disputes arising from the Parambikulam-Aliyar Project (PAP) agreement in India. By incorporating hydrological analysis in the study, the research assesses the potential impacts of proposed solutions on water demand. The GMCR methodology is applied through a comprehensive decision support system (GMCR II), involving the identification of decision-makers, options, and preferences, followed by the development of a conflict resolution model. The analysis is based on a thorough literature review of previous studies on GMCR and PAP systems. The strategic analysis using GMCR II reveals nine stable states, representing feasible resolution scenarios. The study evaluates the real-world implications of various resolution scenarios by assessing their hydrological consequences on demand sites using Water Evaluation and Planning (WEAP). The results provide valuable insights into both conflict resolution and environmental considerations, evaluating various resolution scenarios and their feasibility. The study discusses the practical applicability and long-term effectiveness of the proposed solutions, addressing potential challenges and impacts. For instance, this study examines the potential impacts of new constructions in the PAP system, based on hypothetical data assumptions regarding water divergence and reservoir capacity. The study indicates that such a solution involving new construction can reduce the overall unmet water demand by up to 39%, with a notable decrease of up to 50% in unmet demand for irrigation in Tamil Nadu. However, the study also reveals potential challenges, including a 14% increase in unmet demand for irrigation in Kerala. This study contributes to the existing literature by providing a novel application of GMCR to a complex water management conflict, highlighting its potential to support policymakers in mitigating conflicts and promoting cooperation in the context of transboundary water management. While offering valuable insights into the strategic dynamics of the PAP agreement, the analysis is constrained by limited data availability, such as long-term hydrologic data and real-time water usage data. Future research addressing data scarcity can leverage this study’s framework to develop more robust and actionable management strategies.

An advanced decision support system (DSS) for implementing the Graph Model for Conflict Resolution (GMCR) is designed and illustrated using a real world conflict. The new system, called GMCR+, is capable of handling a wide variety of decision problems involving two or more decision-makers (DMs). Given the DMs, the options or courses of action available to each of them, and each DM’s relative preferences over the possible scenarios or states that could occur, GMCR+ can calculate stability and equilibrium results according to a rich range of solution concepts that explain human behaviour under conflict. Then the inverse component of the DSS GMCR+ can determine what DMs’ preference rankings of states must be in order to produce stable states and equilibria as specified by the user. Other features incorporated into GMCR+ include coalition analysis, graph and tree diagram visualisation, narrative reporting of results and a tracing feature that shows how the conflict could evolve from a status quo state to a desirable equilibrium or other specified outcome. The system GMCR+ has a modular design in order to facilitate the addition of further advancements.

The crucial role of the Graph Model for Conflict Resolution (GMCR) in making wise decisions to resolve complex real-world problems is put into perspective in this important chapter. First, the relationship of GMCR to approaches in game theory is explained, emphasizing how GMCR has been purposely designed to model and analyze real-world conflict efficiently. Second, GMCR is a powerful decision technology for tackling multiple participant-multiple objective decision problems, complementing other formal decision tools within Operations Research and Systems Engineering. Third, when utilized within a system of systems viewpoint and an integrative and adaptive approach to responsible governance, the many benefits of GMCR enable it to address many of the complex problems challenging society. To appreciate this chapter fully, it should be read in combination with Chaps. 1 and 10. As an introduction to Chaps. 3 to 9, it reminds the reader of the big picture of decision-making, which complements the technical aspects of GMCR.

PurposeJapan's decision to release nuclear wastewater into the Pacific Ocean in 2023 has sparked strong opposition at home and abroad. In this study, Graph Model for Conflict Resolution (GMCR) method is adopted to analyze the conflict problem, and reasonable equilibrium solutions are given to solve the conflict event.Design/methodology/approachIn this study, GMCR is adopted to solve the conflict problem. First, identify the key decision-makers (DMs) on the issue of nuclear effluent and the relevant options they might adopt. Second, the options of each DM are arranged and combined to form a set of feasible states. Thirdly, the graph model is constructed according to the change of DM's options, and the relative preference of each DM is determined. Finally, the conflict problem is solved according to the definition of GMCR equilibrium.FindingsDischarging nuclear wastewater into the ocean is not the right choice to solve the problem. Developing more space to store nuclear wastewater is more conducive to the protection of the ocean environment.Practical implicationsIt is undesirable for the Japanese government to unilaterally discharge nuclear wastewater into the ocean. Objectively assessing the radioactivity of nuclear wastewater and the cooperation of relevant stakeholders can better solve this conflict.Originality/valueThe problem arising from Japan's releasing plan is complicated because of a lack of information and the existence of multiple stakeholders, while GMCR can help us with a better view of the current circumstance in the conflict.

A decision support system is designed for providing strategic advice to individuals involved in real-world conflict problems. Conflict is endemic in our world, from disputes within a family to wars between countries, so there is great demand for having a flexible decision support system for systematically investigating a rich range of real world conflicts. The graph model can provide a convenient and effective means to model and analyze a strategic conflict. To take advantage of this opportunity, a computer implemented decision support system based on the matrix representation of the graph model for conflict resolution (GMCR) is proposed in this paper. Although a decision support system, called GMCR II is available for conflict analysis, its coding is difficult to modify or adapt to new analysis techniques and new models. Compared with existing system, the proposed system is more effective and convenient for adapting to new analysis techniques and making codes.

In this paper, our objective is to propose a stability concept within the graph model for conflict resolution (GMCR) that does not require knowledge about preferences of other decision makers (DMs) in the conflict and is flexible to analyze the conflict with variable horizon. For that we propose the use of the maximin decision rule within the GMCR. More specifically, we consider a GMCR with two DMs and introduce the concept of Maximin <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</sub> stability with horizon h for a given DM. The Maximin <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</sub> stability concept was inspired by the notion of limited-move stability with horizon h present in the GMCR literature and it is adequate for modeling cautious DMs in conflicts where they have no knowledge about the other DM's preferences. We establish what is the relationship among the Maximin <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</sub> stabilities for different horizons and the relationship among Maximin <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</sub> stability and other GMCR stability concepts. Finally, we present an application to illustrate the proposed stability concept, namely, a neuroscience technological selection conflict in China.