Two-player incentive compatible outcome functions are affine maximizers

TL;DR

This paper demonstrates that in two-player discrete type spaces, any incentive compatible outcome function can be transformed into an affine maximizer via type space perturbation, establishing the optimality of these results.

Contribution

It proves that all incentive compatible functions in two-player discrete settings can be made affine maximizers through minimal perturbations, using linear algebra and tropical geometry.

Findings

Any incentive compatible outcome can be turned into an affine maximizer.

The results are proven to be the strongest possible in this context.

The approach uses tools from linear algebra and tropical geometry.

Abstract

In mechanism design, for a given type space, there may be incentive compatible outcome functions which are not affine maximizers. Using tools from linear algebra and tropical geometry, we prove that for two-player games on a discrete type space, any given outcome function can be turned into an affine maximizer through a nontrivial perturbation of the type space. Furthermore, our theorems are the strongest possible in this setup.