Truthful approximation mechanisms for restricted combinatorial auctions

When attempting to design a truthful mechanism for a computationally hard problem such as combinatorial auctions, one is faced with the problem that most efficiently computable heuristics can not be embedded in any truthful mechanism (e.g. VCG-like payment rules will not ensure truthfulness). We develop a set of techniques that allow constructing efficiently computable truthful mechanisms for combinatorial auctions in the special case where each bidder desires a specific known subset of items and only the valuation is unknown by the mechanism (the single parameter case). For this case we extend the work of Lehmann, O'Callaghan, and Shoham, who presented greedy heuristics. We show how to use If-Then-Else constructs, perform a partial search, and use the LP relaxation. We apply these techniques for several canonical types of combinatorial auctions, obtaining truthful mechanisms with provable approximation ratios

Weak monotonicity characterizes deterministic dominant-strategy implementation

We characterize dominant-strategy incentive compatibility with multidimensional types. A deterministic social choice function is dominant-strategy incentive compatible if and only if it is weakly monotone (W-Mon). The W-Mon requirement is the following: If changing one agent's type (while keeping the types of other agents fixed) changes the outcome under the social choice function, then the resulting difference in utilities of the new and original outcomes evaluated at the new type of this agent must be no less than this difference in utilities evaluated at the original type of this agent

Mechanism Design Over Discrete Domains

Often, we wish to design incentive-compatible algorithms for settings in which the players’ private information is drawn from discrete domains (e.g., integer values). Our main result is identifying discrete settings in which an algorithm can be made incentive-compatible iff the function it computes upholds a simple monotonicity constraint, known as weak-monotonicity. To the best of our knowledge, this is the first such characterization of incentive-compatibility in discrete domains (such characterizations were previously known only for inherently non-discrete domains, e.g., convex domains). We demonstrate the usefulness of this result by showing an application to the TCP-inspired congestion-control problem presented in [20]

Mechanism Design Over Discrete Domains

Often, we wish to design incentive-compatible algorithms for settings in which the players’ private information is drawn from discrete domains (e.g., integer values). Our main result is identifying discrete settings in which an algorithm can be made incentive-compatible iff the function it computes upholds a simple monotonicity constraint, known as weak-monotonicity. To the best of our knowledge, this is the first such characterization of incentive-compatibility in discrete domains (such characterizations were previously known only for inherently non-discrete domains, e.g., convex domains). We demonstrate the usefulness of this result by showing an application to the TCP-inspired congestion-control problem presented in [20]

Truthful approximation mechanisms for restricted combinatorial auctions

When attempting to design a truthful mechanism for a computationally hard problem such as combinatorial auctions, one is faced with the problem that most efficiently computable heuristics can not be embedded in any truthful mechanism (e.g. VCG-like payment rules will not ensure truthfulness). We develop a set of techniques that allow constructing efficiently computable truthful mechanisms for combinatorial auctions in the special case where each bidder desires a specific known subset of items and only the valuation is unknown by the mechanism (the single parameter case). For this case we extend the work of Lehmann, O'Callaghan, and Shoham, who presented greedy heuristics. We show how to use If-Then-Else constructs, perform a partial search, and use the LP relaxation. We apply these techniques for several canonical types of combinatorial auctions, obtaining truthful mechanisms with provable approximation ratios.Mechanism design Combinatorial auctions Multi-unit auctions Multi-unit combinatorial auctions Approximation algorithms

Characterizing Truthfulness In Discrete Domains

Algorithmic mechanism design [9; 10] focuses on the design of algorithms that aim to achieve global objectives in settings in which the "input" is provided by self-interested strategic players2. This necessitates the design of algorithms that are incentive-compatible (a.k.a. truthful 3) in the sense that players are incentivized via payments to behave as instructed. The most natural approach to designing incentive-compatible algorithms is coming up with an algorithm and an explicit payment scheme that guarantees its incentive-compatibility. However, finding appropriate payments is often a difficult, setting-specific, task, which is mostly achievable for very simple types of algorithms