Daniil Musatov - “Fair division on a graph and of a graph“ | MoCCA’20

The talk “Fair division on a graph and of a graph“ by Daniil Musatov on the Moscow Conference on Combinatorics and Applications at MIPT. Annotation: Fair division is a vast topic that brings attention of mathematicians and economists for decades. The general framework is the following: some set of agents want to split among themselves some set of goods such that some fairness condition is satisfied. An additional network structure may be added to the set of agents as well as to the set of goods. We call the first framework fair division on a graph and the second one - fair division of a graph. In these settings some new notions of fairness emerge. For instance, when a network of agents is specified, local envy-freeness means that every agent values her own bundle more than the bundle of any of her neighbors. In the same setting local proportionality means that every agent thinks that his bundle is at least as valuable as the average of his neighbors’ bundles. When a network of goods is