I want to share the same sentiment as Separatrix. Most prey have their "Intelligence" hidden in their ability to survive... usually traits developed through evolution.... Look at lizards for example... their tails can be removed and regrown so that if an attacker grabs them by the tail and removes it, they can still run off. Or you also have the reptiles that blend into their surroundings.
As stated in another answer, someone of the prey category in the current animal world doesn't really think too much as more of it is instinct. They don't walk up to a pile of grass and go hmmm, this looks tastey but if I eat this, I am down wind and my scent will be carried to the pack of wolves over there.
In your story, you can definitely make it so the prey-predator relationship develops into a chess match with the prey being your "defensive" oriented mind and the Predator being the "offensive" oriented mind like in sports. First you would need each side to develop the ability to critically think. Once that happens, you can pretty much take their mental growth anywhere.
As it was also commented though, this game of chess could very well lead to the fact that a predator would just give up and move on to an easier prey instead of constantly forcing the issue. This is a common trait in predators of all forms. Rapists, murders, thieves, narcissists, and so on and so forth. They target the easy person. A girl walking down the street wearing a skirt all by herself at 1 am with her head buried in the phone and not situationally aware of what is going on around her is MORE likely (please note the more likely and not this definitely will) to fall victim than a woman who is walking down the street, in a skirt, with her head up, all by herself at 1 am. The key difference is that with her head up and aware she is able to pay attention to anything sneaking up on her and be a better deterrent. Unless an attacker is dead set on this particular person (which it does happen), an attacker will more likely wait for an easier target than one that will fight and struggle.
Same can be said about burglary. If you got a dog, chances are, your house won't be broken into because a dog will bark their heads off giving more attention than what a burglar wants. Screen doors are an added layer of security to a house that someone would have to break through just to get to the normal door and can also be a deterrent. The key here is doing things that are a deterrent. That doesn't mean 100% of the time you are safe, but it helps increase the chances.
I could keep going on and on but I think you understand the point I am trying to make... the smarter the potential victim, the less likely they become a victim at all and will eventually be ignored all together as not worth the time.