Funding games: the truth but not the whole truth

  • Authors:

  • Amotz Bar-Noy;Yi Gai;Matthew P. Johnson;Bhaskar Krishnamachari;George Rabanca

  • Affiliations:

  • Department of Computer Science, Graduate Center, City University of New York;Ming Hsieh Department of Electrical Engineering, University of Southern California;Department of Electrical Engineering, University of California;Ming Hsieh Department of Electrical Engineering, University of Southern California;Department of Computer Science, Graduate Center, City University of New York

  • Venue:
  • WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
  • Year:
  • 2012

Quantified Score

Hi-index 0.00

Visualization

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.