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Abstract: The core is a quintessential solution concept for profit sharing in cooperative game theory, and LP-duality theory has played a central role in its study, right from its early days to the present time. However, despite the extensive nature of this work, basic gaps still remain. This talk will summarize the main ideas contained in two recent papers which attempt to fill these gaps:
Paper 1 (https://arxiv.org/pdf/2302.07627.pdf): explores the use of total unimodularity and complementarity for the assignment game and its generalizations. It also introduces the notions of min-max fair, max-min fair and equitable core imputations.
Paper 2 (https://www.sciencedirect.com/science/article/pii/S0899825622000239?via%3Dihub): rectifies the fact that the general graph matching game has an empty core by giving the notion of 2/3-approximate core; once again LP-duality plays a key role.
This talk will be self-contained.
BIO: Vijay Vazirani is currently Distinguished Professor in the University of California, Irvine. A good description of his research appears in the Citation of his 2022 INFORMS John von Neumann Theory Prize. His co-edited book, Online and Matching-Based Market Design, will appear in May 2023.
Zoom (in case want to join virtually):
https://illinois.zoom.us/s/88565753908
Meeting ID: 885 6575 3908
Password: 6281116664