We have just experienced the Covid pandemic for the last 2 years, and society didn’t collapse. In the event of a nuclear war, I think the survivors will come together, rather than turn on each other. Food and gasoline may be rationed, maybe curfews imposed, there could be shortages of various necessities (remember the toilet paper thing?). But most of the people will understand. People tend to get united after an external attack. Think 9/11 or Perl Harbor times 10000.