Abstract
We study the following online problem: at each time unit, one of m identical items is offered for sale. Bidders arrive and depart dynamically, and each bidder is interested in winning one item between his arrival and departure. Our goal is to design truthful mechanisms that maximize the welfare, the sum of the utilities of winning bidders.
We first consider this problem under the assumption that the private information for each bidder is his value for getting an item. In this model constant-competitive mechanisms are known, but we observe that these mechanisms suffer from the following disadvantage: a bidder might learn his payment only when he departs. We argue that these mechanism are essentially unusable, because they impose several seemingly undesirable requirements on any implementation of the mechanisms.
To crystalize these issues, we define the notions of prompt and tardy mechanisms. We present two prompt mechanisms, one deterministic and the other randomized, that guarantee a constant competitive ratio. We show that our deterministic mechanism is optimal for this setting.
We then study a model in which both the value and the departure time are private information. While in the deterministic setting only a trivial competitive ratio can be guaranteed, we use randomization to obtain a prompt truthful \({\it \Theta}(\frac 1 {\log m})\)-competitive mechanism. We then show that no truthful randomized mechanism can achieve a ratio better than \(\frac 1 2\) in this model.
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Bartal, Y., Chin, F.Y.L., Chrobak, M., Fung, S.P.Y., Jawor, W., Lavi, R., Sgall, J., Tichý, T.: Online competitive algorithms for maximizing weighted throughput of unit jobs. In: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 187–198. Springer, Heidelberg (2004)
Chin, F.Y.L., Fung, S.P.Y.: Online scheduling with partial job values: Does timesharing or randomization help? Algorithmica 37(3), 149–164 (2003)
Chrobak, M., Jawor, W., Sgall, J., Tichý, T.: Improved online algorithms for buffer management in QoS switches. In: Albers, S., Radzik, T. (eds.) ESA 2004. LNCS, vol. 3221, pp. 204–215. Springer, Heidelberg (2004)
Englert, M., Westermann, M.: Considering suppressed packets improves buffer management. In: SODA 2007 (2007)
Friedman, E.J., Parkes, D.C.: Pricing wifi at starbucks: issues in online mechanism design. In: EC 2003 (2003)
Goldberg, A.V., Hartline, J.D., Karlin, A.R., Saks, M., Wright, A.: Competitive auctions. In: Games and Economic Behavior (2006)
Hajiaghayi, M.T., Kleinberg, R., Mahdian, M., Parkes, D.C.: Adaptive limited-supply online auctions. In: EC 2005 (2005)
Kesselman, A., Lotker, Z., Mansour, Y., Patt-Shamir, B., Schieber, B., Sviridenko, M.: Buffer overflow management in QoS switches. In: STOC, pp. 520–529 (2001)
Lavi, R., Nisan, N.: Online ascending auctions for gradually expiring items. In: SODA 2005 (2005)
Lavi, R., Nisan, N.: Competitive analysis of incentive compatible on-line auctions. In: ACM Conference on Electronic Commerce, pp. 233–241 (2000)
Li, F., Sethuraman, J., Stein, C.: Better online buffer management. In: SODA 2007 (2007)
Mahdian, M., Saberi, A.: Multi-unit auctions with unknown supply. In: EC 2006 (2006)
Mu’alem, A., Nisan, N.: Truthful approximation mechanisms for restricted combinatorial auctions. In: AAAI 2002 (2002)
Nisan, N., Ronen, A.: Algorithmic mechanism design. In: STOC (1999)
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Cole, R., Dobzinski, S., Fleischer, L. (2008). Prompt Mechanisms for Online Auctions. In: Monien, B., Schroeder, UP. (eds) Algorithmic Game Theory. SAGT 2008. Lecture Notes in Computer Science, vol 4997. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79309-0_16
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DOI: https://doi.org/10.1007/978-3-540-79309-0_16
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