Greig, who is currently part of the All Back to Bowie's show at the Fringe, is using the crowd funding method Kickstarter to raise £10,000 so that shows that find it very hard or impossible to come to the Edinburgh festivals can have their work funded. The fund will also help to pay for Palestinian artists to come to Edinburgh.
His initiative, simply called Welcome to the Fringe, will not only provide cash but will also include help, advice, and mentoring from artists and companies in Scotland.
The Kickstarter campaign (to be found at www.kickstarter.com/projects/307277511/welcome-to-the-fringe) has already raised more than £6000 and, Greig believes, should exceed its target by the end of the Fringe.
Greig said he was determined to find practical ways of bringing Palestinian artistic talent to the Fringe, although not only do visa restrictions by the Israeli government make this difficult, but also the strictures of the UK Border Agency.
"The ultimate aim to generate a long running, replete fund and a support system for Palestinian artists to come to the Fringe and, where possible, to help Israeli artists to reject their state funding in coming to Edinburgh," the Kickstarter campaign says.
Shows backed by the fund could use technology such as Skype to virtually 'stage' a show at the festival next year if travel proves impossible.
The fund is also open to "Israeli makers who refuse state sponsorship", but Greig said he may expand the fund to artists from Syria, African states or other countries where political and social conditions mean travelling to, and performing at, the Fringe is unfeasible.
He was inspired to start the fund, which will need more than the initial £10,000 to work to its full potential, by several factors, but most recently the fate of an Israeli show, The City, which shut down this week after failing to find a new venue once protests closed its first home at the Underbelly.
Greig was one of 50 figures who signed an open letter protesting against the performances of The City by Israeli group Incubator Theatre.
Incubator Theatre receive funding from the Israeli government and the letter, also signed by Scots Makar Liz Lochhead, and many writers and theatre directors, urged Underbelly to close it because of the "current, brutal assault by Israel upon the people of Gaza".
On his blog this week, Greig, who has worked on theatre in Ramallah and the West Bank, wrote: "I was not part of the demonstration.
"For me, the pro-Palestinian point is best made in writing. My anxieties about this affair, and my own part in it, go deeper, though, than a dislike of megaphones.
"I support the cultural boycott and I am in solidarity with my colleagues in Palestine, but seeing a show shut down sits badly with me.
"I feel absolutely no pleasure upon hearing about it. I adore the Edinburgh fringe and one of the things I adore about it is that it is a vast and welcoming festival where everyone can find a place. But this is the problem. Palestinians simply can't find a place. There is no proportionality. There is no equality of access to stages."
He adds: "It dispirits me knowing that my Palestinian theatre making friends are unable to come here and, it dispirits me to think that Israeli theatre makers who are brave enough to reject their government's sponsorship, might be unable to come here as well.
"In the light of all this, I felt the need to do something positive."
Greig adds on the Kickstarter page: "Palestinian voices must be heard on their own terms. Palestinian theatre makers are massively disadvantaged.
"It's important that, in establishing this fund, we are careful to make sure its disbursement recognises this."