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SUMMARY:Existence Questions in Discrete Allocation and Data Exchange [Lect
 ure]
DTSTART:20261103T071500Z
DTEND:20261103T080000Z
DTSTAMP:20261030T013200Z
UID:indico-event-1705@math-events.uni-bonn.de
DESCRIPTION:Speakers: Hannaneh Akrami\n\nExistence questions are central t
 o mathematical economics and theoretical computer science: given desirable
  properties\, is there always an outcome satisfying all of them? This talk
  presents one negative and one positive answer.\nFirst\, we settle the cen
 tral open problem in fair division of indivisible goods. When m items are 
 divided among n agents with monotone valuations\, must there be an EFX all
 ocation\, one in which no agent envies another’s bundle after removing a
 ny single item from it? We show that the answer is no. For n ≥ 3 and m 
 ≥ n + 5\, there are submodular instances with no EFX allocation. The pro
 of reduces the question to Boolean satisfiability\, and the same reduction
  proves existence for n = 3 and m = 7.\nSecond\, we study the exchange of 
 data\, which\, unlike classical goods\, can be copied at no cost. We prove
  that reciprocal and core-stable exchanges always exist for monotone conti
 nuous utilities. The feasible set is not convex\, so standard fixed-point 
 theorems do not apply directly. Instead\, we construct a homeomorphism ont
 o a convex compact set\, apply Brouwer’s theorem\, and pass to a limit.\
 n\nhttps://math-events.uni-bonn.de/event/1705/
LOCATION:Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/1705/
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