(4) If the click probabilities are separable into agent-specific and slot-specific terms, we provide a characterization of MAB mechanisms that are truthful in expectation.
Multi arm bandit games update#
(3) If the search engine has a certain coarse pre-estimate of μij values and wishes to update them during the course of the T rounds, we show that weak pointwise monotonicity and type-I separatedness are necessary while weak pointwise monotonicity and type-II separatedness are sufficient conditions for the MAB mechanisms to be truthful. (2) When the clicks on the ads follow a certain click precedence property, we show that weak pointwise monotonicity is necessary for MAB mechanisms to be truthful. Our contributions include: (1) When μijs are unconstrained, we prove that any truthful mechanism must satisfy strong pointwise monotonicity and show that the regret will be Θ(T) for such mechanisms. In this article, we consider this general case when m > 1 and prove several interesting results. Recent work has focused on the more realistic but non-trivial general case when m > 1 and a few promising results have started appearing. When m = 1, exact characterizations for truthful MAB mechanisms are available in the literature. These mechanisms, due to their connection to the multi-armed bandit problem, are aptly referred to as multi-armed bandit (MAB) mechanisms. Mechanisms for addressing such learning and incentives issues have recently been introduced. A key problem for the search engine therefore is to learn these click probabilities during the initial rounds of the auction and also to ensure that the auction mechanism is truthful. However, the search engine does not know the true values advertisers have for a click to their respective advertisements and also does not know the click probabilities. The search engine would like to maximize the social welfare of the advertisers, that is, the sum of values of the advertisers for the keyword. The Multi Armed Bandit (MAB) problem is a fundamental setting for capturing and analyzing sequential decision making. Mean Field Equilibrium in Multi-Armed Bandit Game with Continuous Reward Xiong Wang1, Riheng Jia2 1The Chinese University of Hong Kong, Hong Kong SAR, China 2Zhejiang Normal University, Jinhua, China, Abstract Mean eld game facilitates analyzing multi-armed bandit (MAB) for a large number of agents. There are click probabilities μij associated with each agent–slot pair (agent i and slot j). A sponsored search auction for a keyword is typically conducted for a number of rounds (say T).
In pay-per-click sponsored search auctions which are currently extensively used by search engines, the auction for a keyword involves a certain number of advertisers (say k) competing for available slots (say m) to display their advertisements (ads for short).
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