An optimal bidimensional multi-armed bandit auction for multi-unit procurement

Bhat, Satyanath and Jain, Shweta and Gujar, Sujit and Narahari, Y (2019) An optimal bidimensional multi-armed bandit auction for multi-unit procurement. In: ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE, 85 (1). pp. 1-19.

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Abstract

We study the problem of a buyer who gains stochastic rewards by procuring through an auction, multiple units of a service or item from a pool of heterogeneous agents who are strategic on two dimensions, namely cost and capacity. The reward obtained for a single unit from an allocated agent depends on the inherent quality of the agent; the agent's quality is fixed but unknown. Each agent can only supply a limited number of units (capacity of the agent). The cost incurred per unit and capacity (maximum number of units that can be supplied) are private information of each agent. The auctioneer is required to elicit from the agents their costs as well as capacities (making the mechanism design bidimensional) and further, learn the qualities of the agents as well, with a view to maximize her utility. Motivated by this, we design a bidimensional multi-armed bandit procurement auction that seeks to maximize the expected utility of the auctioneer subject to incentive compatibility and individual rationality, while simultaneously learning the unknown qualities of the agents. We first work with the assumption that the qualities are known, and propose an optimal, truthful mechanism 2D-OPT for the auctioneer to elicit costs and capacities. Next, in order to learn the qualities of the agents as well, we provide sufficient conditions for a learning algorithm to be Bayesian incentive compatible and individually rational. We finally design a novel learning mechanism, 2D-UCB that is stochastic Bayesian incentive compatible and individually rational.

Item Type:	Journal Article
Publication:	ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE
Publisher:	SPRINGER
Additional Information:	Copyright of this article belongs to SPRINGER
Keywords:	Multi-armed bandit; Mechanism design
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	07 Feb 2019 11:34
Last Modified:	07 Feb 2019 11:34
URI:	http://eprints.iisc.ac.in/id/eprint/61648

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