With this attitude, you won't be able to convince him. He'll expect you to defect, no matter what you say. It's obvious to you what you'll do, and it's obvious for him. By refusing to save a billion people, and instead choosing the meaningless alternative option, you perform an instrumental action that results in your opponent saving 2 billion people. You control the other player indirectly.

Choosing the option other than saving 1 billion people doesn't have any terminal value, but it does have instrumental value, more of it than there is in directly saving 1 billion people.

This is not to say that you can place this kind of trust easily, for humans you may indeed require making a tangible precommitment. Humans are by default broken, in some situations you don't expect the right actions from them, the way you don't expect the right actions from rocks. An external precommitment is a crutch that compensates for the inborn ailments.