Johannes Horner, Massimo Morelli and Francesco Squintani issued a new discussion paper whose title is similar to the title of this post. Longing for peace in my region, I immediately set out to read the paper. Who knows, maybe the peace will come from that paper. What did I find?

There are two parties who fight over a cake of size 1. Each player has a private type, H or L, which is drawn with probability q (for H) and 1-q (for L). There is incomplete information about the type of the other player. If the players agree on a division (x,1-x) of the cake – that’s great. If not, war ensues, and the cake’s size shrinks to theta. Who wins the war? If the two parties have the same type, each has probability 1/2 to win the war. If they have different types, type H wins with probability p>1/2.

This basic model defines a game with incomplete information, and it is a nice exercise to solve it. The trio go on and analyze variations of this basic model. One variation concerns the case where the players can communicate prior to war declaration: each player can send a costless message to the other (about his type). Another variation, from which the title is derived, concerns the introduction of a mediator, who receives private messages from the players and can propose a division or recommend war. The third variation concerns the introduction of an arbitrator who can enforce his recommendation. In addition to solving the various models, the trio shows that an arbitrator who can enforce his recommendation is as effective as a mediator who can only propose self-enforcing agreements. Cool.

After reading the paper I was left with a little sour taste. The model is interesting, I am sure that the equilibrium calculations are not trivial and perfectly executed. But will this paper bring peace to the worn Middle East? I doubt it. First, there is no incomplete information about the other party’s type: after so many years of struggle, each player knows perfectly well the player he is facing. Second, if mediation breaks down, war does not necessarily ensue. Indeed, in 2000 war followed the breakdown in negotiation. But most probably this will not happen in 2011, after the current round of negotiation fails. And after one round of mediation fails, there is always place for another round. And the relative power of the players changes over time: one day Israel attacks a ship that brings food to Gaza and the Palestinians receive points in the international arena, the other day Israel makes some concession and it gains points. The international arena is not modeled at all. And war itself is not the final outcome; it is just one step towards reaching your goal (is the goal an agreement?). This was exhibited nicely by the 1973 war between Israel and Egypt-Syria, that followed negotiations that led to nothing and was followed by the Egypt-Israel peace treaty. The Palestinian’s Intifadas, uprisings against Israeli rule, were also one way to influence Israel’s attitude towards the Palestinians.

We always have to start somewhere, with a simple model that we can analyze. But I fear that this paper will not help Israeli Prime Minister Netanyahu, Palestinian Chairman Mahmoud Abbas, and the American mediators find the formula of peace.