Optimal Multi-unit Combinatorial Auctions with Single Minded Bidders

Abstract

The current art in optimal combinatorial auctions is limited to handling the case of single units of multiple items, with each bidder bidding on exactly one bundle (single minded bidders). This paper extends the current art by proposing an optimal auction for procuring multiple units of multiple items when the bidders are single minded. We develop a procurement auction that minimizes the cost of procurement while satisfying Bayesian incentive compatibility and interim individual rationality. Under appropriate regularity conditions, this optimal auction also satisfies dominant strategy incentive compatibility. The results presented here hold true for equivalent forward auction settings as well.

Optimal Combinatorial Auction for Initial Commitment Decision Problem in Virtual Organizations

“…The quantity which seller i is asked to supply, X i (c i , r i ) is non-increasing in c i ∀r i Proof: A similar theorem is presented by Iyengar and Kumar [11] and Gujar and Narahari [13]. To prove the necessity part of the theorem, we first observe that,…”

“…However, while solving the optimization problem [1], the seller has to ensure the feasibility constraints arising due to single unit of multiple items and the bidders being single minded. Gujar and Narahari [13] have extended the problem to include multi-unit bundles in the combinatorial auctions. In the next section, we develop an optimal combinatorial auction for ICDP in the presence of single minded bidders with associated reputations.…”

“…Ledyards auction, however, does not take into account multiple units of multiple items. Gujar and Narahri [13] have extended the Ledyards auction to the case of procuring multiple units of multiple items for single minded bidders.…”

Privacy Preserving and Cost Optimal Mobile Crowdsensing Using Smart Contracts on Blockchain

“…However, there have been different attempts for specific settings [40], [41], [42]. The key difference between [40], [41] and our settings is, in their paper a mobile user either assigned the set of tasks he is interested in or nothing where as in our settings, the mobile user may get subset of its desirable tasks. In [42], the mobile user needs to submit capcity, that is how many tasks he can perform and the auction may assign any set of tasks not exceeding his capcity.…”

“…Designing optimal combinatorial auctions for general settings is an open problem. However, there have been different attempts for specific settings [40], [41], [42]. The key difference between [40], [41] and our settings is, in their paper a mobile user either assigned the set of tasks he is interested in or nothing where as in our settings, the mobile user may get subset of its desirable tasks.…”