Funding Games: The Truth but Not the Whole Truth

  • Amotz Bar-Noy
  • Yi Gai
  • Matthew P. Johnson
  • Bhaskar Krishnamachari
  • George Rabanca
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7695)

Abstract

We introduce the Funding Game, in which m identical resources are to be allocated among n selfish agents. Each agent requests a number of resources xi and reports a valuation \(\tilde{v}_i(x_i)\), which verifiably lower-bounds i’s true value for receiving xi items. The pairs \((x_i, \tilde{v}_i(x_i))\) can be thought of as size-value pairs defining a knapsack problem with capacity m. A publicly-known algorithm is used to solve this knapsack problem, deciding which requests to satisfy in order to maximize the social welfare.

We show that a simple mechanism based on the knapsack highest ratio greedy algorithm provides a Bayesian Price of Anarchy of 2, and for the complete information version of the game we give an algorithm that computes a Nash equilibrium strategy profile in O(n2 log2m) time. Our primary algorithmic result shows that an extension of the mechanism to k rounds has a Price of Anarchy of \(1 + \frac{1}{k}\), yielding a graceful tradeoff between communication complexity and the social welfare.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Amotz Bar-Noy
    • 1
  • Yi Gai
    • 2
  • Matthew P. Johnson
    • 3
  • Bhaskar Krishnamachari
    • 2
  • George Rabanca
    • 1
  1. 1.Department of Computer Science, Graduate CenterCity University of New YorkUSA
  2. 2.Ming Hsieh Department of Electrical EngineeringUniversity of Southern CaliforniaUSA
  3. 3.Department of Electrical EngineeringUniversity of CaliforniaUSA

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