Speaking of games, cats swatting at other cats (or you) is their idea of a good time. It can also be a cat's way of asserting itself as the dominant feline. As long as there's no hissing, clawing, or other aggressive behavior, you don't really have to worry about it.
It's classic play behavior. Your cat is bored and decided to practice hunting - with you as the prey. If there was a second cat, it would use that as the prey. Unless the cat uses it's claws, it's all in good fun and you can probably make it stop by playing more with it or getting a second cat.
Play aggression is the most common type of aggressive behavior that cats direct toward their owners. It involves typical predatory and play behaviors, including stalking, chasing, attacking, running, ambushing, pouncing, leaping, batting, swatting, grasping, fighting and biting.
Cats attack because it's fun
Cats love to play and attacking is usually just another form of this. Attack play is most common in younger cats who will attack pretty much anything: you, kitten friends, plants, toys, toilet paper rolls, shoes, shadows…you get the idea.
Your cat may be playing or trying to get your attention. I've had more than one cat that would whack me in the face or on my foot and then run away and wait for me to feed them or give them fresh water. One cat would wake me up for breakfast (her breakfast) by gently dragging her paw against my eyelids.
This is called petting induced or overstimulation aggression. It's a common behavior in many cats, and is something that can be both frustrating and frightening until you learn how to manage this behavior with your cat.
When cats display aggression when touched or petted, it can stem from many different motivations. The most common include: Fear/defense: A fearful cat may exhibit dilated pupils, ears turning back, or a twitching tail. In this situation, your cat may growl, hiss or swat at the person reaching, touching or petting.
Play Aggression
If a person's hands and arms are too close to the cat during play, the cat may bite, scratch, and pounce on the person, leading to injuries. Cats may also lunge from under beds during play aggression episodes.
It all comes down to instinct. Why do cats attack feet so often? As Cat Health noted, "Cats chase things because it's innate behavior. They're predators, so it's second nature for them to chase things.
If your cat is kneading you, it is generally a sign that they are very contented and happy, so take it as a compliment! However, it can sometimes hurt if your kitty friend digs in with their nails! If your cat does this, you can try putting a towel or a blanket over your lap to protect it when your cat sits with you.
Bunting or Rubbing: You may notice that sometimes cats will run into their humans like battering rams with their heads or bodies. It's a form of communication for cats.
Believe it or not, this is a common feline behaviour known as petting-induced aggression. Some cats respond to petting with aggressive mannerisms such as biting, scratching, hissing, vocalizing, and even growling. This behaviour is also commonly referred to as overstimulation aggression.
Hugging your arm or leg and biting you is a classic cat hunting move. When cats catch large prey, they will often grasp it with their front legs and then bite it while 'bunny kicking' with their back legs. If your cat is doing this to you, they are misdirecting their hunting behaviour onto you.
Ever gotten the cold shoulder from your cat? Of course, you have! Chances are if you live with a feline, you've had to kiss and make up more than once. The good news is, despite their reputations for being antisocial, cats love bonding and they do forgive and forget.
Cats play in a way that "involves typical predatory and play behaviors," notes the ASPCA: stalking, attacking, clawing and biting their perceived opponent. It's not unusual for them to act this way with their pet parents, and once they're in the throes of roughhousing, they may have difficulty pulling back.
If your cat only attacks when you let out a yelp or a cry, it could be due to noise-induced aggression. A particular frequency can often elicit an aggressive reaction from a cat, such as a person singing, a baby crying, or a person screaming.
Smell Transfer
Cats recognize each other (and us) by scent. Raising the butt is your cat's way of getting their anal glands closer to your nose so you can get a whiff of their pheromones. This is how cats introduce themselves to other cats.
There's a difference between rough play and aggression
During fun play, ears and tails will be straight up in the air. There may be some hissing, but play is usually quiet. If you notice a cat's ears turn toward the back of the head (“airplane ears”) or you hear growling, the play has tipped over into aggression.
It could be that they're trying to communicate something to you, or they might simply be enjoying the sensation of biting and licking you. Cats enjoy positive reinforcement, so if you respond positively to their biting (by petting them or talking to them in a pleasant tone), they're likely to continue doing it.
Some kitty lovers call this a 'love bite', others call it petting aggression. It's a controversial subject but it's believed that if your cat suddenly bites you for no apparent reason, it could be because they are being overstimulated by the constant stroking - which you thought they were enjoying!
Aside from grooming behavior, these little bites are also a sign of affection. For cats, it's completely normal for them to use their teeth with little bites to communicate their love for you.
Don't physically discipline your cat: Training a pet can be very frustrating when you're learning together, but it goes without saying that you should never hurt a cat while disciplining her. Cats are already intolerant of human forms of punishment, but physically dominating a cat will break your bond with her.
It's common for kittens and young cats to engage in rough, active play because all feline play consists of mock aggression. Cats stalk, chase, sneak, pounce, swat, kick, scratch, ambush, attack and bite each other—all in good fun. If they're playing, it's reciprocal. They change roles frequently.
If you've witnessed the average cat being hugged, you've probably seen squirming, meowing, panting, and eventually, claws. Don't take it personally—most cats view hugging as a form of human-induced torture, pleasurable to the human part of the equation only. However, some cats do seem to enjoy it.