Monotone branch-and-bound search for restricted combinatorial auctions

  • Authors:

  • John Lai;David Parkes

  • Affiliations:

  • Harvard University, Cambridge, MA, USA;Harvard University, Cambridge, MA, USA

  • Venue:
  • Proceedings of the 13th ACM Conference on Electronic Commerce
  • Year:
  • 2012

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Abstract

Faced with an intractable optimization problem, a common approach to computational mechanism design seeks a polynomial time approximation algorithm with an approximation guarantee. Rather than adopt this worst-case viewpoint, we introduce a new paradigm that seeks to obtain good performance on typical instances through a modification to the branch-and-bound search paradigm. Incentive compatibility in single-dimensional domains requires that an outcome improves monotonically for an agent as the agent's reported value increases. We obtain a monotone search algorithm by coupling an explicit sensitivity analysis on the decisions made during search with a correction to the outcome to ensure monotonicity. Extensive computational experiments on single-minded combinatorial auctions show better welfare performance than that available from existing approximation algorithms.