Event № 78
I'll consider an optimal partition of resources (e.g. customers) between several agents (e.g. experts), given utility functions for the agents and their capacities. This problem is a variant of optimal transport (Monge-Kantorovich) between two measure spaces where one of the measures is discrete (capacities) and the cost of transport is the utilities of agents. I'll concentrate on the individual value for each agent under optimal partition and show that, counter-intuitively, this value may decrease if the agent's utility is increased. Sufficient and necessary conditions for increment of the individual value will be given, independently of the other agents. The sharpness of these conditions will be discussed, as well.If time permit I'll discuss some applications to cooperative games.