TY - GEN

T1 - Mechanism design on discrete lines and cycles

AU - Dokow, Elad

AU - Feldman, Michal

AU - Meir, Reshef

AU - Nehama, Ilan

PY - 2012

Y1 - 2012

N2 - We study strategyproof (SP) mechanisms for the location of a facility on a discrete graph. We give a full characterization of SP mechanisms on lines and on sufficiently large cycles. Interestingly, the characterization deviates from the one given by Schummer and Vohra (2004) for the continuous case. In particular, it is shown that an SP mechanism on a cycle is close to dictatorial, but all agents can affect the outcome, in contrast to the continuous case. Our characterization is also used to derive a lower bound on the approximation ratio with respect to the social cost that can be achieved by an SP mechanism on certain graphs. Finally, we show how the representation of such graphs as subsets of the binary cube reveals common properties of SP mechanisms and enables one to extend the lower bound to related domains.

AB - We study strategyproof (SP) mechanisms for the location of a facility on a discrete graph. We give a full characterization of SP mechanisms on lines and on sufficiently large cycles. Interestingly, the characterization deviates from the one given by Schummer and Vohra (2004) for the continuous case. In particular, it is shown that an SP mechanism on a cycle is close to dictatorial, but all agents can affect the outcome, in contrast to the continuous case. Our characterization is also used to derive a lower bound on the approximation ratio with respect to the social cost that can be achieved by an SP mechanism on certain graphs. Finally, we show how the representation of such graphs as subsets of the binary cube reveals common properties of SP mechanisms and enables one to extend the lower bound to related domains.

KW - facility location

KW - graphs

KW - mechanism design

UR - http://www.scopus.com/inward/record.url?scp=84863522285&partnerID=8YFLogxK

U2 - 10.1145/2229012.2229045

DO - 10.1145/2229012.2229045

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SN - 9781450314152

T3 - Proceedings of the ACM Conference on Electronic Commerce

SP - 423

EP - 440

BT - EC '12 - Proceedings of the 13th ACM Conference on Electronic Commerce

T2 - 13th ACM Conference on Electronic Commerce, EC '12

Y2 - 4 June 2012 through 8 June 2012

ER -