Bo Lin and Ngoc Mai Tran applied results in tropical geometry to the study of mechanism design (Two-player incentive compatible mechanisms are affine maximizers). They proved that for two-player games on a discrete type space, any given mechanism can be turned into an affine maximizer through a nontrivial perturbation of the type space. In their proof, they connected the incentive compatible mechanisms of a type space T to the tropical determinant of the minors of the matrix T.
Ngoc Mai Tran and François Baccelli derived a tropical version of the result of Kac on the zeros of polynomials with random coefficients (Zeros of Random Tropical Polynomials, Random Polygons and Stick-Breaking).
The common roots of tropical of a class of random polynomials in two variables is analyzed in a recent work by the same authors in Iterated Gilbert Mosaics and Poisson Tropical Plane Curves using a stochastic geometry approach based on iterated random tessellations.