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Ata Atay’s new working papers published

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Ata Atay‘s two recent workings papers have been published and are accessible at the following links:
 
 
Authors: Ata Atay, Ana Mauleon, Vincent Vannetelbosch
 
 
Abstract
Since stable matchings may not exist, we adopt a weaker notion of stability for solving the roommate problem: the bargaining set. Klijn and Massó (2003) show that the bargaining set coincides with the set of weakly stable and weakly efficient matchings in the marriage problem. First, we show that a weakly stable matching always exists in the roommate problem. However, weak stability is not sufficient for a matching to be in the bargaining set. Second, we prove that the bargaining set is always non-empty. Finally, as Klijn and Massó (2003) get for the marriage problem, we show that the bargaining set coincides with the set of weakly stable and weakly efficient matchings in the roommate problem.
Keywords: Roommate problem, matching, (weak) stability, bargaining set
JEL Classifications: C71, C78
Mathematics Subject Classification: 91B68

 

Authors: Ata Atay, Pedro, Calleja, Sergio Soteras
 
 
Abstract
This paper takes a game theoretical approach to open shop scheduling problems with unit execution times to minimize the sum of completion times. By supposing an initial schedule and associating each job (consisting in a number of operations) to a different player, we can construct a cooperative TU-game associated with any open shopscheduling problem. We assign to each coalition the maximal cost savings it can obtain through admissible rearrangements of jobs’ operations. By providing a core allocation, we show that the associated games are balanced. Finally, we relax the definition of admissible rearrangements for a coalition to study to what extend balancedness still holds.
Keywords: Open shop, scheduling, cooperative game theory, core, balancedness
JEL Classification: C44, C71
Mathematics Subject Classification (2010): 90B35, 91A12

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