I think the larger point here is that the government is suppressing protected speech by using private sector actors as intermediaries.

Is there proof the government actually uses this apparatus?

I don't think there's any government involvement necessary here - Mastercard has some censorship apparatus (which they claim to be necessary for their brand's reputation), and they used it (apparently through pressure from an Australian group) towards video games.

This is really bad but I don't think it makes sense to believe a government was ever involved here. Of course, there should be laws put in place to regulate mastercard into a common infrastructure. They should not be able to deny processing a legal payment because of nebulous "brand reputation" reason.

In this case? Not that I know of, but I'm not following closely.

In general? Absolutely - search 'Operation Chokepoint'.

There's a great summary in the middle of this (very long) article under that header: https://www.bitsaboutmoney.com/archive/debanking-and-debunki...

There are laws in place to regulate this behavior, but the government has chosen to protect mastercard from enforcement in this instance. That's the smoking gun.

Mastercard could simply refuse service for those games in particular instead of demanding (through proxies) that the games be banned from Steam. There's a clear antitrust violation.

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if we're going to point to this there are much much more problematic instances of this happening, in particular democratic pressure to platforms like twitter and facebook to suppress certain information as "disinformation" even when it later came out to be true (hunter biden laptop)