Truthful Mechanisms for One-Parameter Agents

The authors show how to design truthful (dominant strategy) mechanisms for several combinatorial problems where each agent's secret data is naturally expressed by a single positive real number. The goal of the mechanisms we consider is to allocate loads placed on the agents, and an agent's secret data is the cost she incurs per unit load. We give an exact characterization for the algorithms that can be used to design truthful mechanisms for such load balancing problems using appropriate side payments. We use our characterization to design polynomial time truthful mechanisms for several problems in combinatorial optimization to which the celebrated VCG mechanism does not apply. For scheduling related parallel machines (Q/spl par/C/sub max/), we give a 3-approximation mechanism based on randomized rounding of the optimal fractional solution. This problem is NP-complete, and the standard approximation algorithms (greedy load-balancing or the PTAS) cannot be used in truthful mechanisms. We show our mechanism to be frugal, in that the total payment needed is only a logarithmic factor more than the actual costs incurred by the machines, unless one machine dominates the total processing power. We also give truthful mechanisms for maximum flow, Q/spl par//spl Sigma/C/sub j/ (scheduling related machines to minimize the sum of completion times), optimizing an affine function over a fixed set, and special cases of uncapacitated facility location. In addition, for Q/spl par//spl Sigma/w/sub j/C/sub j/ (minimizing the weighted sum of completion times), we prove a lower bound of 2//spl radic/3 for the best approximation ratio achievable by truthful mechanism.

Authors

• Aaron Archer
• Éva Tardos

Keywords

• Cost accounting
• Computer science
• Game theory
• Algorithm design and analysis
• Load management
• Polynomials
• Design optimization
• Approximation algorithms
• Power generation economics
• Operations research
• Truthful Mechanism
• Lower Bound
• Estimation Algorithm
• Maximum Flow
• Dominant Strategy
• Load Balancing
• Sum Of Time
• Approximate Ratio
• Affine Function
• Total Payments
• Unit Load
• Logarithmic Factor
• Social Security
• Objective Function
• Data Privacy
• Shortest Path
• Amount Of Work
• Dynamic Programming
• Conditions In Order
• Output Function
• Payment Scheme
• Flow Algorithm
• Makespan
• Allocation Algorithm
• Mechanical Design
• Facility Costs
• Optimal Mechanism
• Results In Areas
• Optimal Schedule
• Optimal Assignment