# Approximately Maximizing the Broker's Profit in a Two-sided Market

## TL;DR

This paper develops mechanisms to maximize broker profit in two-sided markets with private seller values and complex buyer valuations, achieving an 8-approximation of optimal profit through a reduction from production-cost markets.

## Contribution

It introduces a reduction technique converting mechanisms for production-cost markets into approximate mechanisms for two-sided markets, even with general valuation functions.

## Key findings

- Mechanism conversion preserves approximation ratios.
- Achieves an 8-approximation for two-sided market profit.
- Works with general combinatorial valuation functions.

## Abstract

We study how to maximize the broker's (expected) profit in a two-sided market, where she buys items from a set of sellers and resells them to a set of buyers. Each seller has a single item to sell and holds a private value on her item, and each buyer has a valuation function over the bundles of the sellers' items. We consider the Bayesian setting where the agents' values are independently drawn from prior distributions, and aim at designing dominant-strategy incentive-compatible (DSIC) mechanisms that are approximately optimal. Production-cost markets, where each item has a publicly-known cost to be produced, provide a platform for us to study two-sided markets. Briefly, we show how to covert a mechanism for production-cost markets into a mechanism for the broker, whenever the former satisfies cost-monotonicity. This reduction holds even when buyers have general combinatorial valuation functions. When the buyers' valuations are additive, we generalize an existing mechanism to production-cost markets in an approximation-preserving way. We then show that the resulting mechanism is cost-monotone and thus can be converted into an 8-approximation mechanism for two-sided markets.