The zero-sum game is a miserable business. One participant's gains are balanced by the losses of the other: a world of conflict, winners and losers. John Forbes Nash won a deserved Nobel prize in 1994 for developing an alternative - in the 'Nash equilibrium' each party must take into account the decision-making of the other. Two actors, let's call them I and P, make the best decision they can after taking into account the other's decision: mutual recognition, compromise, and 'win-win.'
Tal Becker, the experienced Israeli negotiator, puts the same idea like this: 'it is about having the confidence and courage to think about your negotiating partner's victory speech, not just your own'.
Israel and Palestine struggle to take each other into account. For they are not 'actors' but two traumatised peoples. Painful histories, contested memories, and competing narratives seem to conspire until it is difficult to see the other clearly for themselves. The Israeli novelist Amos Oz has spoken eloquently about this.
You would have thought that two victims of the same oppressor [Europe] would have become brothers, marching together to the barricades, but ladies and gentlemen, in real life some of the worst conflicts are precisely the conflicts between two victims of the same oppressor, two children of the same cruel parent don't love one another, they look at each other and say, 'you are exactly like him', 'you are the image of the oppressing parent', and this is very much the situation between Jew and Arab.
The international community can play the role of honest broker in New York by asking this question of any proposal: what course of action is most likely to empower those willing and able to decisively advance the two-state vision and contribute to a more stable, secure, and peaceful Middle East?
It's a question David Cameron has asked. "We want to see the Palestinians have the dignity of their own state. However, we believe in the two-state solution, so it must be a Palestine alongside a secure Israel. When it comes to the whole issue of recognition, the test for us is: are we doing something that will help to push forward the peace process? That is the most important thing."
The authority of the Prime Minister and Foreign Secretary have been enormously enhanced by the leadership they have shown in supporting the Libyan people in their inspiring struggle for freedom and democracy. They should now encourage an approach to the peace process by the international community that is marked by four features.
Be Humble
The issues are complex and the negotiating will be hard. There are no magic formulas - it took us a long time in Northern Ireland and we are still working it through.
Don't seek to impose peace
No conflict-ending agreement can stick without popular support. Help create an environment conducive to the painful historic compromises and the leap of faith required of the Israeli and Palestinians peoples. Encourage trust and cooperation until each people can 'write the others victory speech.' It is more important to provide carrots than sticks.
Don't make it about personalities
We must be bigger than that. Demonising individuals gets in the way of a fair assessment of the facts.
Do not mislead the parties, be an honest broker with both
We need to be clear with both sides that painful compromise is required. We are able to tell Israel hard truths, rightly, about settlements, but we do not hear the same intensity in our messages to the Palestinians about refugees. President Obama's two speeches in May showed us the way - no party can bypass the other, and the international community should not be 'played' against either party.
In 1994 in Stockholm John Nash was introduced by Karl-Göran Mäler with these words regarding his pioneering insight. 'When there is strategic interaction, the outcome for one agent depends not only on what that agent does, but also very largely on how other agents act or react.' The International community may be tempted to award symbolic victories and humiliating defeats this week. It should resist. For whether it likes it or not, in Nash's terms it is a player in the game and the outcome depends on its ability to steer the parties to take account of each other.