Seriously, why can't we have somewhere that we could just shoot each other for funzies? There's no reason to shoot any Cmdrs in Open Play unless there's a sufficiently high bounty, and I've been playing the game for two weeks and I've only seen ONE player with more than 1000 cred bounty on his/her head.
It doesn't have to be much, just an arena with FFA rules, and you earn a bit of money when you kill someone.
Go to an Anarchy System Nav. Beacon or Conflict Zone in a 'Warzone' System.
You want matchmaking Combat; then wait for Star Citizen, or there are a myriad of Space Combat games on Steam right now that provide this; as the idea of any sort of PVE/PVP Queue breaks immersion and the entire point in nature of Elite.
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This said, I would support the idea of a 'Structured Tournament' aspects; such-as Racing, Non-Lethal Combat, etc... as forms of 'Entertainment' that you could participate in and bet on down the line (very far down the line) if they decide to include 'Customisable Sub-Systems'; so think along the lines of Formula 1 Grand Prix, where there are specific guidelines and the equipment used is specialist (high cost) that is not useful for normal everyday use.
Instead the 'Edge' is created through the different manufacturers, that you then fine tune specifically for your flying style. It could even have lengthy research to boost capabilities slowly over a Season, with each new Season introducing new 'guidelines' and limitations that have to be followed; with the need to gain 'Sponsorship' from Factions that you would then display their Logos on your Hull (with bonus based on how well you do).
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I mean fully flesh this idea out and post it at some point, as if well designed it could add some seriously interesting and highly competitive e-sport (in universe) that could be enjoyable to participate, watch or bet on.