You could run your dishwasher without adding dishwasher detergent.
But your dishes won't be as clean as they would be if you used some dishwasher detergent.
If you don't have dishwasher detergent you can add a bit of regular dish soap or use some powdered laundry detergent to clean your dishes in the dishwasher.
I have used powdered laundry detergent before in my dishwasher and it worked just fine.
So if you have to use the powdered laundry detergent or liquid dish detergent in the dishwasher that's fine as well.
The dishwasher detergent is just made to produce less suds so your dishes get cleaned better in the dishwasher.
But regular dish soap is fine to use in a dishwasher as long as you use it in small enough quantities.