Can Anyone Name This POW Comedy?

Years ago, sometime in the early to mid 80's, I saw a film, or maybe even a TV episode, on cable.

It was a comedy from the 50's or 60's. It was the sort of film that Bob Hope would star in, that type of comedy.

The premise had four people stranded on an island during WWII, two American and two Japanese. One of the sides manages to capture the other. They then realize, due to the Geneva Convention, they have to feed their prisoners. But, there is no food on the island. So, they let the prisoners escape, and try to get captured themselves so they have to be fed.

It goes on and on like this.

I have no memory of the title, and only saw it that once. But I just remembered it and thought I'd throw it out there.

Anyone recognize it?