Notes on Bhattacharya, Conitzer, Kamesh, and Xia, Incentive Compatible Budget Elicitation in Multi-unit Auctions


As with all my scanned notes, this has the usual disclaimer: these posts are just so I can use search engines to easily search for my notes, which are sufficient for me to recall talks and papers but probably not much use to anyone else. Paper here.

In this paper, we consider the problem of designing incentive compatible auctions for multiple (homogeneous) units of a good, when bidders have private valuations and private budget constraints. When only the valuations are private and the budgets are public, Dobzinski {\em et al} show that the {\em adaptive clinching} auction is the unique incentive-compatible auction achieving Pareto-optimality. They further show thatthere is no deterministic Pareto-optimal auction with private budgets. Our main contribution is to show the following Budget Monotonicity property of this auction: When there is only one infinitely divisible good, a bidder cannot improve her utility by reporting a budget smaller than the truth. This implies that a randomized modification to the adaptive clinching auction is incentive compatible and Pareto-optimal with private budgets.
The Budget Monotonicity property also implies other improved results in this context. For revenue maximization, the same auction improves the best-known competitive ratio due to Abrams by a factor of 4, and asymptotically approaches the performance of the optimal single-price auction.
Finally, we consider the problem of revenue maximization (or social welfare) in a Bayesian setting. We allow the bidders have public size constraints (on the amount of good they are willing to buy) in addition to private budget constraints. We show a simple poly-time computable 5.83-approximation to the optimal Bayesian incentive compatible mechanism, that is implementable in dominant strategies. Our technique again crucially needs the ability to prevent bidders from over-reporting budgets via randomization.

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See also, Nisan’s original budget balance paper, and his blog post on this paper.

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Notes on Bhattacharya, Conitzer, Kamesh, and Xia, Incentive Compatible Budget Elicitation in Multi-unit Auctions

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