Characterizing Truthful Multi-Armed Bandit Mechanisms

We consider a multi-round auction setting motivated by pay-per-click auctions for Internet advertising. In each round the auctioneer selects an advertiser and shows her ad, which is then either clicked or not. An advertiser derives value from clicks; the value of a click is her private information. Initially, neither the auctioneer nor the advertisers have any information about the likelihood of clicks on the advertisements. The auctioneer's goal is to design a (dominant strategies) truthful mechanism that (approximately) maximizes the social welfare.

If the advertisers bid their true private values, our problem is equivalent to the \emph{multi-armed bandit problem}, and thus can be viewed as a strategic version of the latter. In particular, for both problems the quality of an algorithm can be characterized by \emph{regret}, the difference in social welfare between the algorithm and the benchmark which always selects the same ``best" advertisement. We investigate how the design of multi-armed bandit algorithms is affected by the restriction that the resulting mechanism must be truthful. We find that truthful mechanisms have certain strong structural properties -- essentially, they must separate exploration from exploitation -- \emph{and} they incur much higher regret than the optimal multi-armed bandit algorithms. Moreover, we provide a truthful mechanism which (essentially) matches our lower bound on regret.

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In  ACM Conference on Electronic Commerce (EC'09)

Publisher  Association for Computing Machinery, Inc.
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