Tamás Király:
Matching games with transferable and non-transferable utility
In the discrete version of the optimal transport problem, optimality can be certified by a simple witness that has a natural interpretation in cooperative game theory as profit sharing between partners. Cooperative games involving the distribution of profit (or utility) among partners are called transferable utility games, and we will discuss some notable examples including matching games as well as games based on other combinatorial optimization problems. The lecture series will also offer an introduction to matching games with non-transferable utility. These include the famous stable marriage problem of Gale and Shapley and its generalizations, as well as more recent solution concepts like nearly stable matchings and popular matchings.