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.
5 comments
August 26, 2010 at 10:41 am
Anonymous
This paper is 52 pages long, a point you raised in your earlier post.
August 26, 2010 at 9:45 pm
michael webster
Why would you think any calculation would help mediators find a resolution?
August 28, 2010 at 1:37 pm
Anon
Better to do this than pointless applied math exercises with no real applications (eg stochastic games with absorbing states and dynamic games with no discounting)- pure mathematicians will find then trivial and scientists will find them useless.
August 28, 2010 at 1:39 pm
Long winded
Hypocrisy of blog author – even longer paper:
http://www.luiss.it/stochastic-workshop/Erice2005/papers/vieille.pdf
August 29, 2010 at 12:27 am
Eilon
The last two comments tell me that I hit a soft spot. The above post says nothing that a referee report might not say. And most responses to the post on long papers were positive. So why did I get such offended (and offending) responses? Is the fact that my research is exercises in applied math, which are useless to economists (and by the way, far from trivial for pure mathematicians), is of relevance? Or is the fact that I wrote a 65-page paper full of useless proofs relevant to the fact many papers in economics are too long? (and believe it or not, this was the longest paper that I wrote, and it was my only paper published in Econometrica. What does this show?)
I am happy to get criticism, but these responses are not criticism. A valid criticism is providing a handful of job market papers that present great ideas that need even 100 pages. Or explaining why my criticism to the paper by the trio is not valid (like the one my Michael Webster). But alas, none such constructive comments were given in the last two responses.