Digraph Competitions and Cooperative Games |
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| Authors: | van den Brink René Borm Peter |
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| Institution: | (1) Department of Econometrics, Free University Amsterdam, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands;(2) CentER and Department of Econometrics and Operations Research, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands |
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| Abstract: | Digraph games are cooperative TU-games associated to domination structures which can be modeled by directed graphs. Examples come from sports competitions or from simple majority win digraphs corresponding to preference profiles in social choice theory. The Shapley value, core, marginal vectors and selectope vectors of digraph games are characterized in terms of so-called simple score vectors. A general characterization of the class of (almost positive) TU-games where each selectope vector is a marginal vector is provided in terms of game semi-circuits. Finally, applications to the ranking of teams in sports competitions and of alternatives in social choice theory are discussed. |
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| Keywords: | Digraph competition cooperative TU-game Shapley value core marginal vector selectope vector simple score vector |
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