Shared IP addresses
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IP addresses can be shared, see Wikipedia's article on Dynamic Host Configuration Protocol for more information.
Major ISPs, like Virgin Media, Comcast and Verizon tend to use DHCP to assign their IPs.
However, there's also a bad side to it too... the trolls and spammers shift their way around the IPs and will generally try and cause havoc for other, legitimate users of the ISP.
Even worse, you can get denial-of-service users, who will attempt to cause attacks on your wiki.
If you need to block, try and keep it short, and block as anonymous users only (unless your MediaWiki version is pre-1.8), possibly allowing account creation - hopefully the problem will be solved.
However, if worst comes to worst, take things to a CheckUser for advice: but only in extreme circumstances (e.g. spambots, vandalbots, mass-account creation)