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Reports (Research Report) Year : 2007

Graphs and Path Equilibria

Abstract

The quest for optimal/stable paths in graphs has gained attention in a few practical or theoretical areas. To take part in this quest this chapter adopts an equilibrium-oriented approach that is abstract and general: it works with (quasi-arbitrary) arc-labelled digraphs, and it assumes very little about the structure of the sought paths and the definition of equilibrium, \textit{i.e.} optimality/stability. In this setting, this chapter presents a sufficient condition for equilibrium existence for every graph; it also presents a necessary condition for equilibrium existence for every graph. The necessary condition does not imply the sufficient condition a priori. However, the chapter pinpoints their logical difference and thus identifies what work remains to be done. Moreover, the necessary and the sufficient conditions coincide when the definition of optimality relates to a total order, which provides a full-equivalence property. These results are applied to network routing.
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Dates and versions

inria-00195379 , version 1 (10-12-2007)

Identifiers

  • HAL Id : inria-00195379 , version 1
  • ARXIV : 0712.1521

Cite

Stéphane Le Roux. Graphs and Path Equilibria. [Research Report] 2007, pp.41. ⟨inria-00195379⟩
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