  Helton and Nie conjectured that every convex semialgebraic set over the field
of real numbers can be written as the projection of a spectrahedron. Recently,
Scheiderer disproved this conjecture. We show, however, that the following
result, which may be thought of as a tropical analogue of this conjecture, is
true: over a real closed nonarchimedean field of Puiseux series, the convex
semialgebraic sets and the projections of spectrahedra have precisely the same
images by the nonarchimedean valuation. The proof relies on game theory
methods.

Algebraic Geometry