# Estimating Approximate Incentive Compatibility

## TL;DR

This paper introduces techniques to estimate how close various mechanisms are to being incentive compatible by analyzing sample data and measuring potential utility gains from misreporting across different auction types.

## Contribution

It presents a novel method for estimating incentive compatibility gaps using finite sample analysis and proves the accuracy of these estimates across diverse auction mechanisms.

## Key findings

- Effective estimation of incentive compatibility gaps from samples.
- Applicability to multiple auction formats including first-price and second-price auctions.
- Theoretical guarantees on the estimation accuracy.

## Abstract

In practice, most mechanisms for selling, buying, matching, voting, and so on are not incentive compatible. We present techniques for estimating how far a mechanism is from incentive compatible. Given samples from the agents' type distribution, we show how to estimate the extent to which an agent can improve his utility by misreporting his type. We do so by first measuring the maximum utility an agent can gain by misreporting his type on average over the samples, assuming his true and reported types are from a finite subset -- which our technique constructs -- of the type space. The challenge is that by measuring utility gains over a finite subset of the type space, we might miss type pairs $\theta$ and $\hat{\theta}$ where an agent with type $\theta$ can greatly improve his utility by reporting type $\hat{\theta}$. Indeed, our primary technical contribution is proving that the maximum utility gain over this finite subset nearly matches the maximum utility gain overall, despite the volatility of the utility functions we study. We apply our tools to the single-item and combinatorial first-price auctions, generalized second-price auction, discriminatory auction, uniform-price auction, and second-price auction with spiteful bidders.