Don't ask me why, but my story's come to a race of zombies coming to blows with a race of skeletons.
The zombies are able to infect live non-zombies. They wander about aimlessly, moving no more than about a mile per hour (roughly a third of normal human walking speed). When they see any non-zombie, they run (that is, two miles per hour) directly toward their target, not taking into account obstacles on the ground. (Note that all of their prey will turn into humanoid zombies, regardless of its original species.) That said, they have claws to climb over that sort of thing. They do have the ability to swim, but it's the same proportions as above: one-third the speed of humans when "inactive" and two-thirds when "active." They have normal blood circulation and are warm-blooded.
Zombies are unable to reproduce; they're comparable to viruses in that they infect hosts with their genetics to create more of their species. They can die, but only if their head is detached from the rest of their body.
They can use weapons (read: anything they can pick up and whack something with), but they only attack in this method if they can't bite their target without rendering them unconscious. Oh, and by the way, the zombies have a mind hive: they can all communicate with each other mentally. They're not your garden-variety braindead zombie; to the contrary, they have excellent brain capacity.
Now here's the catch. Zombies are able to turn themselves into humans for about thirty seconds, after which they turn back into zombies. There's a half-hour cooldown on this ability. When posing as humans, they have normal human capabilities, though most notably the fact that they can move significantly faster than they could otherwise.
The skeletons, on the other hand, can move at normal speed all the time. Unlike the zombies, who take no defensive measures while scouring for live prey, the skeletons are able to hide. They can see infrared waves as well as normal light waves. They have their own "chatter" language to communicate, and they are able to strategize to capture their prey. Because they can communicate and strategize so effectively, they can give each other boosts over walls.
They are able to deconstruct the bones in their body and use them as weapons or tools, but they can only control the bones directly or indirectly attached to their skull. They cannot die, but cutting off every bone from the upper skull essentially takes away any method of attack. They cannot reattach lost limbs.
Skeletons are able to reproduce, but they are also able to infect non-skeletons. (Unlike the zombies, though, the prey will retain its original species. Thus, many skeletons are able to fly, and many are forced to swim.)
The Big Question
Assume that these species live on a planet exactly like ours today, and they fight in the middle of a big city where there's lots of prey (say, NYC). Their primary goal is to defeat the enemy, and if they have the option between attacking the enemy and attacking a nearby human/pigeon, they'll attack the enemy.
Which species has the upper hand? What are each species' dominant strategies? (I'm an aspiring mathematician; bonus points for identifying Nash Equilibria under these circumstances.)
Why this is on-topic
For those who voted to put this on hold, this bit is my response. From the help center:
Capabilities of characters...are on-topic, but questions must focus on what is possible or likely to develop, not what someone would or should do.
That is exactly my question. Given the capabilities of my characters, what is "likely to develop"?