Even though LP-duality has played a central role in the study of the core, right from its early days to the present time, basic gaps still remain. I will summarize three papers which address these gaps:


Paper 1   defines new matching-based games, with important applications, and characterizes their cores.

It also gives efficient algorithms for computing core imputations with enhanced fairness properties: min-max fair, max-min fair and equitable core imputations.


Paper 2  extends the scope of the notion of core beyond profit --- equivalently cost or utility --- sharing. 

The game in this paper is not a cooperative game, it is a game against nature.


Paper 3  rectifies the fact that the general graph matching game has an empty core by giving the notion of 2/3-approximate core.


This talk will be self-contained. 


Video Recording