I spent much of last week being a Palestinian. And not just any Palestinian. I was the man charged with negotiating their future. Over the course of two full days I was Saeb Erekat, longtime (and now caretaker) negotiations chief of the Palestine Liberation Organisation, facing off against an Israeli team led by one of Binyamin Netanyahu's closest confidants. Behind closed doors, and under the watchful eye of Barack Obama's handpicked envoy, George Mitchell, we argued and haggled over the knottiest issues of the Israeli-Palestinian conflict – seeking to find common ground on questions of rights, refugees and recognition as well as security and sovereignty.

I succeeded in extracting from the Israelis an acceptance that the states of Palestine and Israel will be separated by a border reflecting the 1967 lines, more or less, and that Jerusalem will serve as the capital of both nations. Which I considered a rather good week's work.

Strictly speaking, the names above should all come wrapped in quotation marks. For I was playing the role of Erekat in an elaborate simulation game – alongside a dozen or so people whose professional lives are steeped in the conflict, whether as diplomats, NGO officials, scholars or journalists, from both inside and outside the region. Participants were asked to step outside their comfort zone.

We were under Chatham House rules – so no names I'm afraid – but I can tell you that my fellow "Palestinian" negotiators included an Israeli citizen who is a full-time advocate for his country, a senior official of a pro-Israel charity, and a top figure from the Jewish Chronicle. Representing Israel were two Palestinians – one a citizen of the US, the other a citizen of Israel – and two luminaries of London-based NGOs with long experience of the occupied territories. Crucially, both teams could call on coaches – one Israeli, one Palestinian – who had served as negotiators at high-level peace talks. Holding the ring was a serving European diplomat whom we all had to address as Senator Mitchell.

The scheme is the brainchild of an American academic, Natasha Gill, who calls it "Track 4" to distinguish it from the three more conventional tracks of diplomacy: those involving government-to-government talks, civil society, or people-to-people encounters. Her aim is not to have a "peacenik lovefest", in which each side learns to empathise with the other, but rather to understand the dynamics, and difficulties, of the negotiations themselves.

I admit I had deep fears, starting with a dread of embarrassment – speaking as one for whom the words "role play" are second only to "audience participation" in their ability to chill the blood. So what happened once we were in the room?

Attached to the track dealing with rights and recognition, I found myself intransigent in defending the right of Palestinian refugees from 1948 to return to their homes in what is now Israel. What is more, my colleagues and I gave short shrift to the "Israeli" delegation's protestations of sorrow for the refugees' plight that came attached to a refusal to take any responsibility for it. My team-mate – whose day job has him pushing Israel's case around the clock – accused one "Israeli" interlocutor of failing to understand the nature of Palestinian identity, half-forgetting that she was, in fact, Palestinian. When the "Israelis" repeatedly insisted that we recognise Israel as a Jewish state, our irritation rose further. No such demand had been made for past peace agreements: to demand it now was surely a wrecking tactic.

Our vehemence seemed to pay off. When it came to drafting a US text, "Mitchell" produced a document giving us much that we wanted, starting with those 1967 lines and Jerusalem. The Israelis put up some resistance, but buckled on those two key points.

I would like to tell you that this was a product of our canny negotiating skills, but I can't. Apparently, this is how it almost always turns out. Gill has noticed a repeating pattern. No matter whom she casts as the Palestinian delegation, they fast become impassioned and eloquent, full of righteous indignation. "Even pro-Israel Zionists become angry Palestinians," she says. Conversely, she adds, the Israeli teams often struggle, giving away too much too quickly. Even when they strain hard, they become moderates at best.

Some cynics will suspect that reveals the inherent bias of those who have acted as Israelis in Track 4: they're so pro-Palestinian, they can't put themselves in Israeli shoes. But Gill locates the explanation in the nature of the competing claims. The "Palestinians" walk into the room regarding themselves as the aggrieved, injured party. They are the underdog, the occupied people, and that gives them the immediate moral high ground.

The Israelis have a narrative involving dispossession and suffering too, but it tends to relate to the past, even if it is the relatively recent past. They are unavoidably cast as the stronger party, the one that wants to hold on to what it has, the one that has to say no. What is more, the "Israelis" soon realise that their cards consist of tangible assets – starting with land – which they are being asked to give up for abstract declarations – on, for example, recognition of Israel – from people they hardly trust. This mismatch eventually feeds their resentment and makes them dig in their heels.

These were valuable lessons in themselves, but the exercise taught something much deeper. Within hours, I noticed that I was becoming fixated on scoring points rather than solving problems. I had a troublesome member of the delegation, constantly positioning himself as more radical, more faithful to the cause – reminding me of the political price I would pay if I compromised too much. This constrained me.

I also realised that the key audience was not really the Israelis across the table – it was the Americans at the head that mattered. It was their text I wanted to influence. In this context, the omission of some phrase the Israelis wanted counted as a victory: it made more sense to avoid an issue than to solve it.

If this is how I behaved after less than 24 hours, no wonder the two sides act the way they do. Gradually I became aware of the enormous gulf that separates those of us who view the conflict from afar – whether from our perch on liberal newspapers or in well-meaning thinktanks – from those who have actually to solve the problem. From this distance, the solution might seem painfully obvious: any cool-headed moderate can see where the midpoint between the two sides lies. But that is to reckon without the pressures on the negotiators within their own team, from a public opinion always ready to cry sell-out, and from the US. And that's even before you get to the demands of the other side.

Gill dreams of creating a "community of shadow negotiators" – people around the world who understand not the narrative of the other so much as the predicament of the peacemakers themselves. It is a noble aim, one that would serve as a corrective to the armies of outsiders whose current contribution is simply to fuel the anger of the two sides, rather than to find a way out – inflaming grievances rather than finding solutions. What's needed are people who understand the price that has to be paid and who are ready to support it.

Those apart from this conflict who claim to care about one or both peoples should take note. There is no shortage of friends of the Israelis or advocates of the Palestinians. What's missing are friends of peace itself.