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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
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
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"?

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closed as off-topic by Hohmannfan, SJuan76, Aify, bilbo_pingouin, Frostfyre Jun 27 '16 at 13:31

This question appears to be off-topic. The users who voted to close gave these specific reasons:

If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ Can skeletons infect dead animals Like a giant skeleton-dinosaur ? I think if skeletons are smart enough to learn how to repair bones then they will surelly win $\endgroup$ – Lenis Sanguinem Jun 27 '16 at 0:05
  • $\begingroup$ Zombies they have hive mind, they are real smart or like fishes smart?, in some sense fishes also hiveminded. So are they able to complex strategies as whole. Can they learn as whole, or they just react? And why they can't use tools. If they are just turtle version of human but with hive mind, which can learn - my bet on zombies, if they do not loose in begin, in long run they will win. $\endgroup$ – MolbOrg Jun 27 '16 at 2:29
  • $\begingroup$ Their best strategy is to swarm their target(s) until they're turned into zombies and join the hive. So intelligence-wise, they're closer to fish-smart. They just choose not to use tools - they'd much rather force their prey to join the swarm than to kill them. $\endgroup$ – user21719 Jun 27 '16 at 2:43
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    $\begingroup$ You just asked a slightly more elaborate version of "Pirates vs Ninjas". en.wikipedia.org/wiki/Pirates_versus_Ninjas And the answer is exactly the same: completely undeterminable because there are so many unknown confounding factors involved. $\endgroup$ – MichaelK Jun 27 '16 at 7:35
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    $\begingroup$ So, the zombies have an intelligent hive mind but for some reason just wander around when not in battle? Why? If they're intelligent why isn't the hive-mind thinking of what it will need for coming battles and having it's members gather resources, build fortifications, collect weapons, lay landmines etc? Why is an intelligent entity acting stupid? Why isn't the horde farming cattle/rats/chickens to convert into humanoid zombies? $\endgroup$ – Murphy Jun 27 '16 at 11:01
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All those zombies and skeletons in NYC, but no one sees them ? ;)

Lets consider these two scenarios:

  1. They all fight it out in a big open field

    The zombies already have the advantage because they are stronger (durability wise, don't know about the zombies and skeletons strengths) than the skeletons. Bones are brittle, and will break from one strong smash. Even if skeletons all armed themselves with weapons beforehand, it will be hard to cut off a zombie-head with those weapons. Not to mention using bones as weapons, as they are blunt weapons - and not particularly strong ones either. The zombies (if smart enough) can even wear some armour while it will be hard for skeletons (they won't fit properly). Hence, the zombies will definitely win here. No Nash Equilibrium over here, just plain old charge-and-kill.

  2. They have time to prepare

    The zombies may have a hive mind, but the skeletons have their own language. So, I think the skeletons are smarter. A particularly smart one will start to convert everything it can into skeletons - birds, small animals, humans, etc. The zombies don't realise because they are staying away from the skeletons and are dumb anyways. Then, after a while the skeletons can release their army of skeleton rats and birds to attack the zombies :) . Imagine if a bunch of skeleton-hawks are carrying something heavy and drop it on those zombies. Even if all the original skeletons are killed, the zombies won't be able to hit those flying skeletons, who will stay away and continue to drop things on the zombies. The skeletons probably won't win outright, but they can continue to chip away at the zombies until they are weakened enough to fight openly (ALL zombies vs. ALL skeletons). If the skeletons prepare, by stocking up on weapons and armours, then they definitely win. Otherwise, they just have a (big) advantage (depending on how much they reduce the zombies) Nash Eq, the zombies probably won't figure out the skeletons plans.

    The skeletons can use all sorts of scenarios - they can use some expendable skeletons (small animals) to lure the zombies into one place, then the humanoid skeletons can drop heavy stuff on them. (Assuming they get up into a building and kill/convert all those people and drop all heavy stuff from the balconies onto those zombies below).

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Let's look at the strengths of both armies, (I assume that both armies are the same sizes)

Zombies

  1. Have a hive mind
  2. Will never have to worry about miscommunication
  3. Among the troops the whole army will react as one to every attack.

Skeletons

  1. Cannot die
  2. Can hide
  3. Can run.
  4. Can repair themselves

So my money is on the skeletons. In a straight fight they will last longer, they are also unable to die, but the zombies can die to blow to the head. And because the skeletons can hide they can also set up an ambush. And if all else fails, at least they can run away unlike the zombies in order to regroup and arm themselves with more weapons.

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  • $\begingroup$ Skeletons can't exactly repair themselves; like I said, once a limb's detached, it can't be glued back on. Although they can't die, if you knock their skull off and knock the bottom jaw off of the skull (so that it can't bite any zombies that get close) it's essentially dead. $\endgroup$ – user21719 Jun 27 '16 at 2:45
  • $\begingroup$ @DonielFilreis from what you said I thought the skeletons could use weapons or at least there bones as weapons. $\endgroup$ – Bryan McClure Jun 27 '16 at 3:34
  • $\begingroup$ @DonielFilreis you said "bones in their body and use them as weapons or tools" If they are capable use their bones as tools then they must be able to use other thing like axes and hammers. And since there faster they can use these things more effectively then any zombie can. $\endgroup$ – Bryan McClure Jun 27 '16 at 3:37