# Ivan Martino: Cooperative game on simplicial complexes

**Time: **
Tue 2020-02-18 11.00 - 11.50

**Lecturer: **
Ivan Martino, KTH, Stockholm

**Location: ** Institut Mittag-Leffler, Seminar Hall Kuskvillan

### Abstract

After shortly recalling the notion of cooperative games and Shapley values, I will define and study probabilistic values for cooperative games on simplicial complexes.

Inspired by the work of Weber "Probabilistic values for games", I will establish the new theory step by step, following the classical axiomatization, i.e. using the linearity axiom, the dummy axiom, etc.

The goal of the talk, if time allows, is to introduce the Shapley values on simplicial complexes generalizing the classical notion in literature. Remarkably, the traditional axiomatization of Shapley values can be extended to this general setting for a rather interesting class of complexes that generalize the notion of vertex-transitive graphs and vertex-homogeneous simplicial complexes. In this talk, I review the results in the manuscript: arXiv:2001.05820, arXiv:2001.00779, and arXiv:2001.00366.