The one who initiated the date (and also therefore chose the restaurant). I will offer to pay for my share, but I have never experienced that a guy who asked me out suggested to split it.
A while into dating though, I'll try to offer other things. Like if he's paid for drinks and we share a taxi back, I'll just pay for it before he has the chance.
Most of the time I'm dating guys a few years older who's already working and they'll never let me (still a student) pay for anything.
I've been dating a guy who's from an insanely rich French family and I try to chip in now and then just to assure him I'm not dating him for the money/that he pays for me.
I'm generally into traditional gender roles. A lot of guys claim that women want the best parts of equality only. Although that is true for some (perhaps for British women), it is not true for all, and slightly unfair. I am not supportive of the current radical feminist society and I didn't ask for it. I am traditional all the way, and I am not a feminist. I take care of a boyfriend, I like to cook for him and I think both parties have a responsibility for the other, even if their 'roles' are different. Naturally I attract men with the same traditional view. For the last guys I've dated, they have either paid the bill while I'm in the bathroom or they do it while I'm there, and refuse to let me look at it.