Martial arts can certainly be a factor in the typical "cyberpunk" game. One of the features of most cyberpunk settings is the increased influence of the Japanese and Chinese, and wherever their influence is felt that strongly, the martial arts are likely to prosper. The fact that cyberpunk worlds tend to be extremely violent places where people need to learn how to fight well doesn't hurt, either.
One way to "customize" martial arts for cyberpunk games is to give some of the styles new names in the cyberpunk patois. For example, Dirty Infighting might be known as "Street Smarts," or Kenjutsu might be known as "Sami Danse." This sort of thing helps to blend martial arts into the campaign so that they seem like an actual part of the world around the characters, not just a tool for the PCs to use.
Of course, one of the important questions in a cyberpunk setting is how to integrate technology and martial arts. This can be done in several ways. Straight cyber-enhancement of Characteristics has a clear advantage for the martial artist: Added STR, DEX, SPD and (perhaps best of all) resistant defenses will make a martial artists of any style a much more dangerous opponent. Beyond that, martial artists can obtain cybergear that provides abilities that are used in conjunction with martial arts. Built-in edged weapons can be awfully handy, especially when they are usually concealed. Superleap, extra running, enhanced senses, clinging, and even such esoteric abilities as Stretching can all be of great use to a martial artist in a cyberpunk setting.
Perhaps the most interesting capability in a cyberpowered world is technologically enhanced or enabled Skills. This could range from computer-enhanced targeting systems (which would add to your Range Modifiers or OCV) to "martial arts chips"
that you can plug in your head to learn a new Maneuver or add Skill Levels. While such Skills are easy to buy if the GM allows it (Skills through a Focus), their use in a campaign should be carefully monitored. If everyone can buy a Kung Fu chip, then Kung Fu loses some of its appeal.
One interesting way to keep this in check: make "chip martial arts" a distinctive Style Disadvantage, and let players with the right Skills recognize and be able to thwart that style fairly easily. Chip martial artists probably shouldn't be allowed to buy Skill Levels with their chip martial arts, because they don't really "know" them. If they want to get better martial arts, they have to buy a new chip; they can't add new maneuvers or DCs or Skill Levels without a new chip. And of course, the chips are limited to the skill of the martial artist the chips are modeled after. It's quite possible that even the best chip you can buy isn't as good as the best martial artist. "I taught that chip everything it knows, but not everything I know."
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