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Annals of Operations Research

, Volume 254, Issue 1–2, pp 211–234 | Cite as

Lexicographic allocations and extreme core payoffs: the case of assignment games

  • Marina Núñez
  • Tamás SolymosiEmail author
Original Paper

Abstract

We consider various lexicographic allocation procedures for coalitional games with transferable utility where the payoffs are computed in an externally given order of the players. The common feature of the methods is that if the allocation is in the core, it is an extreme point of the core. We first investigate the general relationships between these allocations and obtain two hierarchies on the class of balanced games. Secondly, we focus on assignment games and sharpen some of these general relationships. Our main result shows that, similarly to the core and the coalitionally rational payoff set, also the dual coalitionally rational payoff set of an assignment game is determined by the individual and mixed-pair coalitions, and present an efficient and elementary way to compute these basic dual coalitional values. As a byproduct we obtain the coincidence of the sets of lemarals (vectors of lexicographic maxima over the set of dual coalitionally rational payoff vectors), lemacols (vectors of lexicographic maxima over the core) and extreme core points. This provides a way to compute the AL-value (the average of all lemacols) with no need to obtain the whole coalitional function of the dual assignment game.

Keywords

Assignment game Extremal core allocations Average lexicographic value 

Mathematics Subject Classification

91A12 91B68 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of Mathematical Economics, Finance and Actuarial SciencesUniversity of BarcelonaBarcelonaSpain
  2. 2.MTA-BCE ‘Lendület’ Strategic Interactions Research Group, Department of Operations Research and Actuarial SciencesCorvinus University of BudapestBudapestHungary

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