Operations Research Transactions

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The $\tau$-value of Cooperative Games Restricted by Graph

 WANG  Wen-Wen, SUN  Hao, HAN  Wei-Bin   

  • Received:2011-01-26 Revised:2011-09-07 Online:2011-12-15 Published:2011-12-19

Abstract: We first study the  $\tau$-value for graph-restricted games and provide its explicit construction.
The one-point solution could be considered as a natural extension of the  $\tau$-value introduced by
Tijs for classical cooperative games. When the cooperation graph is complete, the  $\tau$-value for
graph-restricted games coincides with the  $\tau$-value for classical cooperative games. Then we
provide an axiomatization of the  $\tau$-value for graph-restricted games via component efficiency,
 relative invariance under S-equivalence and restricted proportionality. The last section introduces
 the  $\tau$-value for two special classes of graph-restricted games.

Key words: graph-restricted games, $\tau$-value, quasibalanced, component efficiency