Since there's a lot of highly motivated individuals who really do want e-sports to work in Australia, the best bet IMO would be to actually create a governing body which isn't motivated by money. The Association would be a for the players by the players style thing, holding online tournaments and offline tournaments all around Australia. They could have a small yearly membership fee and the members could vote on who would head the association, as well as other key roles such as secretary/treasury/Sponsorship liaison... They could vote on venues, tournaments, tournament styles, map pools... All manner of things. You would have to write up a quite substantial list of tournament rules etc. with reasonable punishments etc.
In order to compete in the events you would have to pay the membership fee, which would help the association with sorting venues/prize pools, attracting sponsors/marketing etc.
I mean a few motivated people setting up a non-profit governing body for the players by the players is the only true way that e-sports will kick off in Australia... IMO...
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