  We initiate the representation theory of the degenerate affine periplectic
Brauer algebra on $n$ strands by constructing its finite-dimensional calibrated
representations when $n=2$. We show that any such representation that is
indecomposable and does not factor through a representation of the degenerate
affine Hecke algebra occurs as an extension of two semisimple representations
with one-dimensional composition factors; and furthermore, we classify such
representations with regular eigenvalues up to isomorphism.
