Funding Games: the Truth but not the Whole Truth

TL;DR

This paper introduces the Funding Game, a resource allocation model where agents report lower bounds of their true valuations, and analyzes the efficiency of simple greedy algorithms, showing a tradeoff between communication rounds and social welfare.

Contribution

It presents a new resource allocation mechanism with provable bounds on efficiency and provides algorithms for equilibrium computation and multi-round extensions.

Findings

Bayesian Price of Anarchy is 2 with the greedy mechanism.

Complete information Nash equilibrium can be computed efficiently.

Multi-round extension improves Price of Anarchy to 1 + 1/k.

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 $x_i$ and reports a valuation $\tilde{v}_i(x_i)$, which verifiably {\em 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 {\it 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 $O(n^2 \log^2 m)$ 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.