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Contention Resolution under Selfishness

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Abstract

In many communications settings, such as wired and wireless local-area networks, when multiple users attempt to access a communication channel at the same time, a conflict results and none of the communications are successful. Contention resolution is the study of distributed transmission and retransmission protocols designed to maximize notions of utility such as channel utilization in the face of blocking communications.

An additional issue to be considered in the design of such protocols is that selfish users may have incentive to deviate from the prescribed behavior, if another transmission strategy increases their utility. The work of Fiat et al. (in SODA ’07, pp. 179–188, SIAM, Philadelphia 2007) addresses this issue by constructing an asymptotically optimal incentive-compatible protocol. However, their protocol assumes the cost of any single transmission is zero, and the protocol completely collapses under non-zero transmission costs.

In this paper we treat the case of non-zero transmission cost c. We present asymptotically optimal contention resolution protocols that are robust to selfish users, in two different channel feedback models. Our main result is in the Collision Multiplicity Feedback model, where after each time slot, the number of attempted transmissions is returned as feedback to the users. In this setting, we give a protocol that has expected cost Θ(n+clogn) and is in o(1)-equilibrium, where n is the number of users.

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Notes

  1. Recall from the earlier description that the threat of Fiat et al. requires that all remaining players will be transmitting in every step with probability 1 for a large number of steps. This is an equilibrium only when the cost of a transmission is zero.

  2. Alternatively, we can assume that player transmits with p it =0 on all subsequent rounds.

  3. Notice that since the feedback is symmetric, h it =h jt implies H it =H jt .

  4. Since we are interested in symmetric protocols, then the average expected cost is equal to the expected cost of any player, and hence the social utility coincides with the individual utility.

  5. In fact, if the identities of the players were common knowledge, then simply transmitting in lexicographic order would be incentive-compatible and achievable.

  6. A player i who is currently assigned a leave slot keeps transmitting until she succeeds. This technical detail ensures that the protocol will not collapse if some other player j tries to transmit at that slot. Such an event would occur only if j deviated from the protocol by transmitting in the leave slot assigned to i.

  7. It may reduce by two if the player that succeeded during the split belonged to a group of size 2. The other player in that group would be assigned a leave slot in the same round.

  8. More details can be found in the full-version of [8], at www.cs.tau.ac.il/~urinadav/papers/JournalSelfishMac.pdf

  9. As opposed to a player that the protocol instructs to stay quiet during s with probability 1.

  10. At round 0 all players belong to the same group, i.e., M 0=1.

  11. Validation slots only happen if there is at least one player from G j,k that is supposed to transmit in them. Thus, a player cannot have a successful transmission by attacking a validation slot.

  12. If none of the members of G j,k transmitted during the split slot, then i has a successful transmission. If all members but one transmitted, then the cheating does not get caught (and i only had a failed transmission). In this case, it looks as if all members of G j,k transmitted, and the validation slot is skipped. In all other cases, i gets caught.

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Acknowledgements

The first author was partially supported by DFG grant Kr 2332/1-3 within Emmy Noether Program and by EPSRC grant EP/F069502/1. The second author was supported in part by an NSF Graduate Research Fellowship, NSF grant 0937060 to the Computing Research Association for the CIFellows Project, and NSF grant 1004416.

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Authors and Affiliations

  1. University of Liverpool, Liverpool, UK

    George Christodoulou

  2. California Institute of Technology, Pasadena, CA, USA

    Katrina Ligett

  3. Technische Universität München, München, Germany

    Evangelia Pyrga

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  1. George Christodoulou
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  2. Katrina Ligett
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  3. Evangelia Pyrga
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Correspondence to Evangelia Pyrga.

Additional information

A preliminary version of this work appeared in ICALP 2010.

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Christodoulou, G., Ligett, K. & Pyrga, E. Contention Resolution under Selfishness. Algorithmica 70, 675–693 (2014). https://doi.org/10.1007/s00453-013-9773-4

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