Optimal Robust Mechanism in Bilateral Trading

TL;DR

This paper develops a robust mechanism design for bilateral trade with unknown joint distributions, establishing a deterministic, dominant strategy incentive compatible mechanism that maximizes expected gains under minimal distributional assumptions.

Contribution

It introduces an optimal robust mechanism framework that is deterministic, DSIC, and ex-post IR, with explicit pricing and equivalence to efficiency guarantees.

Findings

Optimal robust mechanism is deterministic and posted-price.

Mechanism is dominant strategy incentive compatible.

Explicit expression for the optimal posted-price.

Abstract

We consider a model of bilateral trade with private values. The value of the buyer and the cost of the seller are jointly distributed. The true joint distribution is unknown to the designer, however, the marginal distributions of the value and the cost are known to the designer. The designer wants to find a trading mechanism that is robustly Bayesian incentive compatible, robustly individually rational, budget-balanced and maximizes the expected gains from trade over all such mechanisms. We refer to such a mechanism as an optimal robust mechanism. We establish equivalence between Bayesian incentive compatible mechanisms (BIC) and dominant strategy mechanisms (DSIC). We characterise the worst distribution for a given mechanism and use this characterisation to find an optimal robust mechanism. We show that there is an optimal robust mechanism that is deterministic (posted-price), dominant strategy incentive compatible, and ex-post individually rational. We also derive an explicit expression of the posted-price of such an optimal robust mechanism. We also show the equivalence between the efficiency gains from the optimal robust mechanism (max-min problem) and guaranteed efficiency gains if the designer could choose the mechanism after observing the true joint distribution (min-max problem).