Dear Jon
Sorry for my late answer. Actually I found my own method. That's not actually I looked for but it worked for my case.
I set the assignee field readonly for the first initial problem page and then create a hidden field which will set the assignee as login user.
<PDM_IF "$args.id" == "0">
<PDM_IF "$args..." = "X">
<INPUT TYPE=hidden NAME=SET.assignee VALUE='$cst.id'>
<PDM_ELIF "$args..." = "Y">
<INPUT TYPE=hidden NAME=SET.assignee VALUE='$cst.supervisor_uuid.id'>
</PDM_ELSE>
</PDM_IF>
As I said not the desired solution but for now it works.
Thank you all for the ideas and support
BR
Utku