  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.
