I want to build a kind of guess game. I do not know the right name but the concept of the game is: person-1(P-1) thinks a name(of anything) and person-2 will have to predict that name by asking as less questions as possible. For example:

p1: thinks something(Steve jobs)

p2: Are you talking about man?

p1: yes.

p2: Is he/she media guy?

p1: No

P2: is he tech personality?

p1: yes

p2: steve jobs.

p1: yes.

So p2 has to ask 4 questions. It could be even more as number of predictors are infinite. Now I want to model this scenario. My Goal is to reduce the number of question. Note that the number of predictors are limited. So situation is not that broad.

I can think of decision tree. But question is, how can I decide where to split so that length of the brunch will be small.

Any suggestion/reference will be appreciated.