SOME EXCESS-BASED SOLUTIONS FOR COOPERATIVE GAMES WITH TRANSFERABLE UTILITY

Krishna Chaitanya Vanam () and N. Hemachandra ()
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Krishna Chaitanya Vanam: S&P Capital IQ, Survey No. 12P, Kondapur Village, Hyderabad, 500 081, India
N. Hemachandra: Industrial Engineering and Operations Research, IIT Bombay, Powai, Mumbai, 400 076, India

International Game Theory Review (IGTR), 2013, vol. 15, issue 04, 1-14

Abstract: For a finite player cooperative cost game, we consider two solutions that are based on excesses of coalitions. We define per-capita excess-sum of a player as sum of normalized excesses of coalitions involving this player and view it as a measure of player's dissatisfaction. So, per-capita excess-sum allocation is that imputation that minimizes the maximum per-capita excess-sums of players. We provide a closed form expression for an allocation, which is the per-capita excess-sum allocation if it is also individually rational. We propose a finite step algorithm to compute per-capita excess-sum allocation for a general game. We show that per-capita excess-sum allocation is coalitionally monotonic. Next, we consider excess-sum solution wherein a player views entire coalition's excess as a measure of dissatisfaction. This excess-sum solution also has above properties. In addition, we consider a super set of core and show that excess-sum allocation can be viewed as an imputation that is a certain center of this polyhedron. We introduce a class of cooperative games that can model cost sharing among divisions of a firm when they buy items at volume discounts. We characterize when excess-based allocations coincide with Shapley value, nucleolus, etc. in such games.

Keywords: Min–max; coalitional monotonicity; approximate core; cost sharing; Shapley value; nucleolus; 91A12; 91B32; 90C47 (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2013
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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DOI: 10.1142/S021919891340029X

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