Digraph Competitions and Cooperative Games

Theory and Decision 53 (4):327-342 (2002)
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
Keywords Digraph competition  cooperative TU-game  Shapley value  core  marginal vector  selectope vector  simple score vector
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