Herve Moulin: Fair Division and Counterfactual-proofness

Herve Moulin, Donald J. Robertson Chair of Economics at the Adam Smith Business School at the University of Glasgow gave a talk at the International Laboratory of Decision Choice and Analysis research seminar on the topic of "Fair Division and Counterfactual-proofness"

Herve Moulin was presenting his findings on his most recent research.

Dividing valuable objects must often take place without cash changing hands: think of family heirlooms among siblings, shifts among interchangeable workers, seats in overbooked classes to students, or computing resources in peer-to-peer platforms.

We assume additive utilities, and that we can divide a limited number of objects, by time-sharing or randomization. The two prominent microeconomic solutions are the Relative Equivalent (REG) solution, and the Nash MaxProduct NMP) (aka the Competitive Equilibrium with Equal Incomes (CEEI) solution, or the Proportionally fair division). With three or more participants, NMP outperforms REG: unlike the latter, NMP meets the No Envy property and all agents benefit from the addition of new objects; and NMP is often “integral” (does not divide any object).

Moreover the NMP rule induces truthful reports if preference about objects an agent receives are verifiable ex post, so that misreporting affects only the objects lost to this agent. Together with Efficiency, Symmetry and Scale Invariance, this Counterfactual-proofness property characterizes the NMP rule.

The talk was attended by HSE faculty and students.