Advances in Cooperative Game Theory

Rafael Herrera studied Mathematics at the National Autonomous University of Mexico (UNAM) and earned his PhD in Mathematics from the University of Oxford. He held various appointments in the USA at Yale University, the University of California at Riverside and the City University of New York, before joining CIMAT in 2005. His research initially centered on Geometry and Topology, and later expanded to include applications of Differential Geometry in Computer Science and Applied Mathematics, particularly in numerical methods, machine learning and optimization. He has published dozens of research papers, supervised numerous undergraduate and graduate theses, and led several externally funded research projects.Throughout his career, Dr. Herrera has received prestigious fellowships and distinctions from institutions such as Worcester College (Oxford University),the Guggenheim Foundation, the Japan Society for the Promotion of Science, and the Berlin Einstein Foundation. He has been a member of the Mexican Academy of Sciences since 2009. He has visited several international institutes including the Max Planck lnstitut für Mathematik, the lnstitut des Hautes Études Scientifiques, the Abdus Salam lnternational Centre for Theoretical Physics, the Scuola lnternazionale Superiore di Studi Avanzati, the Centre de Recerca Matematica and Centro Internacional De Métodos Numéricos en la Ingeniería. He has also played an active role in organizing academic events, editing lecture note volumes, and teaching across a wide range of mathematical subjects. Beatriz Rumbos earned her undergraduate degree in Mathematics from the National Autonomous University of Mexico (UNAM). She holds a Ph.D. in Mathematics from McGill University and a Ph.D. in Economics from Texas A&M University.Following an eight-year tenure at the Institute of Mathematics at UNAM, she joined the Department of Mathematics at the Instituto Tecnológico Autónomo de México (ITAM) in 1996 as a full-time faculty member. In 2010, she was appointed Dean of the Division of Exact Sciences.Dr. Rumbos has served as a visiting scholar at Texas A&M University, McGill University, and the University of Toronto. Her extensive research portfolio includes publications in non-commutative rings, quantum logic, economic dynamics, and decision theory. In addition to her research, she has authored several mathematics textbooks and co-authored a series of children’s books designed to introduce fundamental economic concepts.

• Characterization of Solutions in Axiomatic Form.- Group Representation Ideas Applied to Cooperative Game Theory.- Graphs and Games.- Solutions for Bankruptcy Problems related to Solution Concepts for cooperative Games.- Sharing Costs.- Games with Coalitional Externalities and Axiomatic Characterization of Solutions.- Cooperative Nested Games.