Allocating Positional Goods: A Mechanism Design Approach

I study the optimal allocation of positional goods, where consumers' concern for relative consumption creates externalities.

Applications include luxury goods, priority services, education, and organizational hierarchies.

Using a mechanism design approach, I characterize feasible allocations through a majorization condition.

Under Myerson regularity, the revenue-maximizing mechanism fully separates participating buyers, with possible exclusion at the bottom.

Selling a single level guarantees at least half the maximum revenue.

When all buyers are served, restricting the seller to a single level increases consumer surplus under an increasing failure rate (IFR).

When the seller is restricted to a single level, expanding coverage also benefits consumers under IFR but may harm them otherwise.

I also characterize the welfare-maximizing mechanism with and without subsidies.