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International Workshop on Algorithms and Computation

WALCOM 2012: WALCOM: Algorithms and Computation pp 217–228Cite as

Nash Equilibria with Minimum Potential in Undirected Broadcast Games

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7157))

Abstract

In this paper, we consider undirected network design games with fair cost allocation. We introduce two concepts Potential-Optimal Price of Anarchy (POPoA) and Potential-Optimal Price of Stability (POPoS), where POPoA is the ratio between the worst cost of Nash equilibria with optimal potential and the minimum social cost, and POPoS is the ratio between the best cost of Nash equilibria with optimal potential and the minimum social cost, and show that

  • The POPoA and POPoS for undirected broadcast games with n players are \(\mathrm{O}(\sqrt{\log n})\).

  • The POPoA and POPoS for undirected broadcast games with |V| vertices are O(log|V|).

  • There exists an undirected broadcast game with n players such that POPoA, \(\mathrm{POPoS} = \Omega(\sqrt{\log\log n})\).

  • There exists an undirected broadcast game with |V| vertices such that POPoA,POPoS = Ω(log|V|).

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Author information

Authors and Affiliations

  1. University of Tokyko, Japan

    Yasushi Kawase & Kazuhisa Makino

Authors
  1. Yasushi Kawase
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  2. Kazuhisa Makino
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Editor information

Editors and Affiliations

  1. Graph Drawing and Information Visualization Laboratory, Department of Computer Science and Engineering, Bangladesh University of Engineering and Technology, Bangladesh

    Md. Saidur Rahman

  2. , Faculty of Engineering, Department of Computer Science, Gunma University, 1-5-1 Tenjin-Cho, 376-8515, Kiryu-Shi, Japan

    Shin-ichi Nakano

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Kawase, Y., Makino, K. (2012). Nash Equilibria with Minimum Potential in Undirected Broadcast Games. In: Rahman, M.S., Nakano, Si. (eds) WALCOM: Algorithms and Computation. WALCOM 2012. Lecture Notes in Computer Science, vol 7157. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28076-4_22

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  • DOI: https://doi.org/10.1007/978-3-642-28076-4_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28075-7

  • Online ISBN: 978-3-642-28076-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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