  We have computed Wilsonian effective action in a simple model containing
scalar field with quartic self-coupling which interacts via Yukawa coupling
with a Dirac fermion. The model is invariant under a chiral parity operation,
which can be spontaneously broken by a vev of the scalar field. We have
computed explicitly Wilsonian running of relevant parameters which makes it
possible to discuss in a consistent manner the issue of fine-tuning and
stability of the scalar potential. This has been compared with the typical
picture based on Gell-Mann-Low running. Since Wilsonian running includes
automatically integration out of heavy degrees of freedom, the running differs
markedly from the Gell-Mann-Low version. However, similar behavior can be
observed: scalar mass squared parameter and the quartic coupling can change
sign from a positive to a negative one due to running which causes spontaneous
symmetry breaking or an instability in the renormalizable part of the potential
for a given range of scales. As for the issue of fine-tuning, since in the
Wilsonian approach power-law terms are not subtracted, one can clearly observe
the quadratic sensitivity of fine-tuning measure to the change of the cut-off
scale.
