Researchers upend auction theory with stagewise rational rental games

A new paper from Technion researchers Batya Berzack, Rotem Oshman, and Inbal Talgam-Cohen tackles a fundamental dynamic mechanism design problem: renting an indivisible asset over n days to agents who arrive daily with private valuations. The twist? Agents are stagewise individually rational (IR)—they reject any rental agreement that results in temporary negative utility, even if overall utility would be positive. This matches real-world behavior where users won't accept a partial loss for a later gain, a constraint often ignored in classic models.

The authors show that the optimal rental mechanism can be framed as a sequence of dynamic auctions with seller costs. But stagewise IR shatters conventional auction theory: Myerson's Lemma does not apply, truthful mechanisms are not necessarily monotone, and payments deviate from Myerson's unique payment rule. The team develops alternative characterizations for optimal mechanisms under objectives like welfare maximization, revenue maximization, and consumer surplus. In some cases they can still leverage Myerson's rule; in others they build from scratch. This work highlights that even single-parameter rental games raise rich, classical-unexpected questions—and provides a foundation for designing fair, efficient dynamic markets.