# Bifurcation Mechanism Design -- From Optimal Flat Taxes to Improved Cancer Treatments

## TL;DR

This paper explores how bifurcation phenomena can be harnessed to design mechanisms that improve system performance, demonstrated through flat taxes for social welfare and innovative cancer treatments.

## Contribution

It introduces bifurcation-based mechanisms that leverage system instabilities to achieve better outcomes in social and medical applications.

## Key findings

- Flat taxation can enhance social welfare by destabilizing inefficient equilibria.
- Bifurcation mechanisms can lead to improved cancer treatment strategies.
- Transient parameter changes can induce permanent beneficial system states.

## Abstract

Small changes to the parameters of a system can lead to abrupt qualitative changes of its behavior, a phenomenon known as bifurcation. Such instabilities are typically considered problematic, however, we show that their power can be leveraged to design novel types of mechanisms. Hysteresis mechanisms use transient changes of system parameters to induce a permanent improvement to its performance via optimal equilibrium selection. Optimal control mechanisms induce convergence to states whose performance is better than even the best equilibrium. We apply these mechanisms in two different settings that illustrate the versatility of bifurcation mechanism design. In the first one we explore how introducing flat taxation can improve social welfare, despite decreasing agent "rationality", by destabilizing inefficient equilibria. From there we move on to consider a well known game of tumor metabolism and use our approach to derive novel cancer treatment strategies.