We study the problem of allocating multiple items to two agents whose cardinal preferences are private information. If money is available, Bayesian incentive compatibility and ex-ante Pareto efficiency can be achieved using the Expected Externality Mechanism (EEM). Absent money, under certain reasonable conditions, Bayesian incentive compatibility and ex-post Pareto efficiency remain achievable with a modified EEM that uses one good as a numeraire in lieu of money. We study this modified EEM’s properties and compare it with other allocation procedures.
Aperjis, Christina, Maciej Kotowski, and Richard Zeckhauser. "Efficient Division When Preferences are Private: Using the Expected Externality Mechanism." HKS Faculty Research Working Paper Series RWP19-014, April 2019.