Answer and Explanation:
You: I can tell by the look in your eyes that you're thinking of eating me.
Tiger: That's true. I am indeed.
You: Well, I'd like to advise you against that. If you eat me, your chances of surviving afterwards will diminish.
Tiger: I doubt that. If I eat you, I will gain strength. Consequently, I'll be able to survive for a few more days. That might be enough for a ship to show up and rescue me.
You: That reasoning is good, but flawed. Yes, you will gain strength that will last for a few days. However, if a ship does not show up in a few days, you will die. Fishing is not one of your abilities as a tiger, so you won't catch anything to eat after devouring me. Also, if a ship does show up, the crew may very well be afraid of taking you with them for fear that you might attack and eat them.
Tiger: I see... go on.
You: If you keep me alive, we will solve all of those issues. I can fish for the both of us. We'll both maintain our strength until a ship shows up, even if it takes long. When that happens, they will certainly take us in. I will vouch for you, letting them know you were civilized enough not to eat me. Therefore, they can trust you not to eat them.
Tiger: I see your point, and it is a good one. I promise not to eat you if you promise to keep your word.
You: I promise. We have a deal.