Average-Case Analysis of Mechanism Design with Approximate Resource Allocation Algorithms

Mechanism design provides a useful practical paradigm for competitive resource allocation when agent preferences are uncertain. Vickrey-Clarke-Groves (VCG) mechanism offers a general technique for resource allocation with payments, ensuring allocative efficiency while eliciting truthful information about preferences. However, VCG relies on exact computation of optimal allocation of resources, a problem which is often computationally intractable. Using approximate allocation algorithms in place of exact algorithms gives rise to a VCG-based mechanism, which, unfortunately, no longer guarantees truthful revelation of preferences. Our main result is an average-case bound, which uses information about average, rather than worst-case, performance of an algorithm. We show how to combine the resulting bound with simulations to obtain probabilistic confidence bounds on agent incentives to misreport their preferences and illustrate the technique using combinatorial auction data. One important consequence of our analysis is an argument that using state-of-the-art algorithms for solving combinatorial allocation problems essentially eliminates agent incentives to misreport their preferences.