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)


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 x i and reports a valuation \(\tilde{v}_i(x_i)\), which verifiably lower-bounds i’s true value for receiving x i 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(n 2 log2 m) 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.


Nash Equilibrium Social Welfare Knapsack Problem Valuation Function Nash Equilibrium Strategy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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