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

Nunez, Marina and Solymosi, Tamás (2014) Lexicographic allocations and extreme core payoffs: the case of assignment games. Working Paper. Corvinus University of Budapest Faculty of Economics, Budapest.

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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 relationship 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 relationship. Our main result is 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. As byproducts, we show 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. This provides a way to compute the Alexia value (the average of all lemacols) with no need to obtain the whole coalitional function of the dual assignment game.

Item Type:Monograph (Working Paper)
Series Name:Corvinus Economics Working Papers - CEWP
Series Number / Identification Number:2014/15
Uncontrolled Keywords:assignment game, extremal core allocations, Alexia value
JEL classification:C71 - Cooperative Games
Subjects:Mathematics, Econometrics
Projects:ECO2011-22765 of the Spanish Ministry of Science and Innovation, 2014SGR40 of the Government of Catalonia, COST Action IC1205 on Computational Social Choice, OTKA K-101224, Monumetum Programme (HAS) LD-004/2010
ID Code:1722
Deposited By: Ádám Hoffmann
Deposited On:09 Oct 2014 14:42
Last Modified:17 Oct 2014 08:15

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