Regularized Proportional Fairness Mechanism for Resource Allocation Without Money
Abstract: Mechanism design in resource allocation studies dividing limited resources among self-interested agents whose satisfaction with the allocation depends on privately held utilities. We consider the problem in a payment-free setting, with the aim of maximizing social welfare while enforcing incentive compatibility(agents cannot inflate allocations by misreporting their utilities). The well-known proportional fairness (PF) mechanism achieves the maximum possible social welfare but incurs an undesirably high exploitability (the maximum unilateral inflation in utility from misreport and a measure of deviation from IC). In fact, it is known that no mechanism can achieve the maximum social welfare and exact incentive compatibility (IC) simultaneously without the use of monetary incentives (Cole et al., 2013). Motivated by this fact, we propose learning an approximate mechanism that desirably trades-off the competing objectives. The mechanism is parameterized by an innovative neural network architecture tailored to the resource allocation problem, which we name Regularized Proportional Fairness Network (RPF-Net). RPF-Net is designed to regularize the output of the PF mechanism by a learned function approximator of the worst-case misreported utilities, with the aim of reducing the incentive for any agent to misreport. We derive generalization bounds that guarantee the mechanism performance when trained under finite and out-of-distribution samples and experimentally demonstrate the merits of the proposed mechanism compared to the state-of-the-art.
The PF mechanism acts as an important benchmark for comparing the social welfare of any mechanism. However, there exists no established way of computing its exploitability. The challenge here is that we need to find the maximizer of an optimization problem in which the gradient is only implicitly defined. We for the first time provide a systematic method for finding such (sub)gradients, which enables the exploitability evaluation of the PF mechanism.
Submission Length: Long submission (more than 12 pages of main content)
Assigned Action Editor: ~Michael_Bowling1
Submission Number: 3235
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