IEOR seminars occur on Mondays throughout the fall semester in room 3108 of Etcheverry Hall. Seminars feature leading-edge research from experts in industrial engineering and operations research who come from local, national, and international institutions. Seminars are open to students, faculty, and the public.

Talk Title: LP-Duality Theory and the Cores of Games

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. We address these gaps using the following building blocks from LP-duality theory:

1. Total unimodularity (TUM).
2. Complementary slackness conditions and strict complementarity.
3. Total dual integrality (TDI).

This talk will summarize the main ideas contained in three recent papers:

• Paper 1 explores (1) and (2) and introduces the notions of min-max fair and max-min fair core imputations.
• Paper 2 explores (3) and extends the scope of the notion of core beyond profit — equivalently cost or utility — sharing.
• Paper 3 rectifies the fact that the general graph matching game has an empty core by giving the notion of 2/3-approximate core; again LP-duality plays a central role.

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.