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Timing Matters: Online Dynamics in Broadcast Games

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Web and Internet Economics (WINE 2018)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 11316))

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Abstract

This paper studies the equilibrium states that can be reached in a network design game via natural game dynamics. First, we show that an arbitrarily interleaved sequence of arrivals and departures of players can lead to a polynomially inefficient solution at equilibrium. This implies that the central controller must have some control over the timing of agent arrivals and departures in order to ensure efficiency of the system at equilibrium. Indeed, we give a complementary result showing that if the central controller is allowed to restore equilibrium after every set of arrivals/departures via improving moves, the eventual equilibrium states reached have exponentially better efficiency.

Part of this work was done when all the authors were visiting Microsoft Research - Redmond. Partial support for this work was provided by the following grants: S. Chawla from NSF grants CCF-1101429 and CCF-1320854; S. Naor from ISF grant 1585/15 and BSF grant 2014414; D. Panigrahi from NSF grants CCF-1527084 and CCF-1535972, an NSF CAREER Award CCF-1750140, and faculty research awards from Google and Yahoo; M. Singh from NSF grant CCF-1717947; S. Umboh from ERC consolidator grant 617951 and NSF grant CCF-1320854.

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Notes

  1. 1.

    The full version of this paper [12] provides examples illustrating these bounds.

  2. 2.

    Observe that when an agent arrives or makes an improving move, paths of other agents may become suboptimal for them.

  3. 3.

    Charikar et al. also studied a variant where arrivals happen in uniformly random order and are interleaved with adversarially ordered best response moves. For this setting, they were able to prove an upper bound of \(O(\sqrt{n}{\text {polylog}}n)\) on the quality of the equilibria reached, but did not present any lower bounds.

  4. 4.

    Another bound is the optimal Steiner tree on all vertices for which an agent arrived at some point in the dynamics. Since we can assume metric costs, we can restrict our attention to these vertices and then mst cost is within a factor of two of the cost of optimal Steiner tree.

  5. 5.

    Note that although arrivals within a single epoch are simultaneous in that every arriving player picks a best response path with respect to the equilibrium state at the beginning of the epoch, arrivals in different epochs are sequential. In this sense our model captures sequential arrivals with interleaved improving moves.

  6. 6.

    Because of this comparison against the mst, we prefer the term “broadcast game” for this setting, rather than the “multicast game”.

  7. 7.

    The existence of a cycle would imply that one of the agents can improve her cost share by switching to a different path and the current state is not an equilibrium.

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Author information

Authors and Affiliations

  1. Computer Sciences Department, University of Wisconsin - Madison, Madison, USA

    Shuchi Chawla

  2. Department of Computer Science, Technion, Haifa, Israel

    Joseph (Seffi) Naor

  3. Department of Computer Science, Duke University, Durham, USA

    Debmalya Panigrahi

  4. H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, USA

    Mohit Singh

  5. School of Information Technologies, The University of Sydney, Sydney, Australia

    Seeun William Umboh

Authors
  1. Shuchi Chawla
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  2. Joseph (Seffi) Naor
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  3. Debmalya Panigrahi
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  4. Mohit Singh
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  5. Seeun William Umboh
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Corresponding author

Correspondence to Debmalya Panigrahi .

Editor information

Editors and Affiliations

  1. University of Liverpool, Liverpool, UK

    George Christodoulou

  2. Universität Augsburg, Augsburg, Germany

    Tobias Harks

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Chawla, S., Naor, J.(., Panigrahi, D., Singh, M., Umboh, S.W. (2018). Timing Matters: Online Dynamics in Broadcast Games. In: Christodoulou, G., Harks, T. (eds) Web and Internet Economics. WINE 2018. Lecture Notes in Computer Science(), vol 11316. Springer, Cham. https://doi.org/10.1007/978-3-030-04612-5_6

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  • DOI: https://doi.org/10.1007/978-3-030-04612-5_6

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