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Game Theory for Control of Optical Networks pp 121–142Cite as

Games in Network Topologies

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Part of the book series: Static & Dynamic Game Theory: Foundations & Applications ((SDGTFA))

Abstract

This chapter provides approaches on how to deal with games in more complicated network topologies, starting from the basic games in single point-to-point WDM fiber links studied in Chap. 7. The multi-link topologies studied are representative for selected paths extracted from a mesh configuration in which no closed loops are being formed by channel optical paths. In network configurations, coupled constraints are propagated along fiber links and constraint functions become complicated from the end-to-end point of view. The non-convexity introduces additional complexities for analysis. In this chapter, we present a partition approach. More precisely, we partition the general multi-link structure into stages each stage being a single link. Then we formulate a partitioned Nash game for general multi-link topologies composed of ladder-nested stage Nash games. We also show that convexity is ensured in single-sink topologies, so that a partition approach could be based on single-sink stages.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Toronto, Toronto, ON, Canada

    Lacra Pavel

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  1. Lacra Pavel
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Correspondence to Lacra Pavel .

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© 2012 Springer Science+Business Media New York

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Pavel, L. (2012). Games in Network Topologies. In: Game Theory for Control of Optical Networks. Static & Dynamic Game Theory: Foundations & Applications. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-8322-1_8

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