## Department of Mathematics

Indian Institute Of Technology Madras , Chennai

### Computing the nucleolus for Assignment games and Cyclic permutation games

#### Abstract :

While the Shapley value and the nucleolus are two unique solution concepts for any cooperative transferable utility games, in general , computation of them is NP hard. We concentrate on two subclasses that stem from real estate models and queueing models called the assignment game and the permutation game. They both have non empty cores and one can get the core of permutation games from the core of an associated assignment game. However algorithms to determine the nucleolus for assignment games involve only its essential coalitions, that are just the singletons and buyer- seller pairs . Unfortunately the essential coalitions for a general permutation game can explode to the order of $0(2^{|N|})$. For the special class of cyclic permutation games , it is possible to determine the nucleolus as its minimal balanced collections are closely related to rook moves with reverse intervals forming balanced collections with symmetric weights. The talk should be of interest to researchers in Economics, Computer science, Management science and Combinatorists.

Key Speaker Dr. T.E.S. Raghavan, Prof. Emeritus, Dept. of Mathematics, Statistics and Computer Science College of Liberal Arts & Sciences University of Illionis, Chicago
Place NAC 522
Start Time 3:00 PM
Finish Time 4:00 PM