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This book examines the use of third-party mediation as a conflict resolution method. In an attempt to explain why some, but not all, conflicts are mediated, this work argues that diverse conflict structures are inherently different in their susceptibility to mediation attempts. By offering a systematic method for measuring the transformability of conflict structures, this book contributes to our understanding of the sufficient and necessary conditions for mediation. In addition, the study offers an analytical framework for the examination of mediation as a trilateral rational bargaining process. Although the general concept of mediation as a three-person game is not new, most studies focus on either the disputants' perspectives or the mediator's perspective. In contrast, this study integrates the perspectives of all three parties. The framework links the different stages involved in the whole process of mediation, from the onset of mediation, through the mediation strategies used, to the outcome, rather than focusing on one particular aspect. The book applies the framework to two case studies - the conflict between Israel and Egypt and the conflict between India and Pakistan - and provides new insights into these conflicts from a mediation perspective. In general, the model developed here provides a framework for systematically assessing conflicts and the options available to those involved in the mediation process.