**Peter Biró**Research Professor at the Simons Laufers Mathematical Sciences Institute

Banatao Auditorium | 310 Sutardja Dai Hall

Wednesday, November 1, 2023, 2-3 PM

We study housing markets (Shapley and Scarf, 1974) and show that for strict preferences the unique strong core allocation “respects improvement”: if an agent’s object becomes more desirable for some other agents, then the agent’s allotment in the unique strong core allocation weakly improves. We extend this result to weak preferences for both the strong core (conditional on non-emptiness) and the set of competitive allocations (using probabilistic allocations and stochastic dominance). There are no counterparts of the latter two results in the two-sided matching literature. Respecting improvements is an important property for applications of the housing markets model such as kidney exchange: it incentivises each patient to bring the best possible set of donors to the market. We conduct computer simulations using markets that resemble the pools of kidney exchange programmes. We compare the game-theoretical solutions with current techniques (maximum size and maximum weight allocations) in terms of violations of the respecting improvement property. We find that game-theoretical solutions fare much better at respecting improvements, even when exchange cycles are bounded, and they do so at a low efficiency cost. As a stepping-stone for our simulations, we provide novel integer programming formulations for computing core, competitive, and strong core allocations.

This is a joint work with Flip Klijn, Xenia Klimentova, and Ana Viana.

#### Speaker Bio

Péter Biró graduated with an MSc in Mathematics at Budapest University of Technology and Economics in 2003, and then received his PhD in Mathematics and Computer Science at the same institute in 2007. During this period, he also studied economics for five years at Corvinus University of Budapest, graduating with MSc in 2007. Afterwards, he was a postdoctoral fellow at the Computer Science Department, University of Glasgow for three and a half years. In 2010 he moved back to Budapest, and since then he has a research position at the Institute of Economics, KRTK, Hungarian Academy of Sciences, which was later renamed to Eötvös Loránd Research Network. From 2010 to 2016 he worked in the Game Theory research group, and in 2016 he established his own research group on Mechanism Design, funded by the Momentum Grant of the Hungarian Academy of Sciences. He also teaches part time at the OR Department, Corvinus University of Budapest since 2013. He was on sabbatical from the Budapest positions twice, first in 2014 as a visiting professor at the Economics Department, Stanford University invited be Al Roth for a year, and then in 2023, when he co-organised and participated in a 4-month program at Simons Laufer Mathematical Sciences Institute, Berkeley, USA. His research interest lies in the interdisciplinary fields of Market Design, Engineering Economics, and in particular matching problems under preferences. In his research he uses multiple approaches including game theory, algorithm theory, graph theory, and optimisation. Besides theoretical studies, he has been involved in several practical applications, such as the UK kidney exchange programme, the Scottish resident allocation scheme, and the Hungarian higher education admission scheme.