Peace and Game Theory

Tyler Cowen, known co-conspirator of those Volokhs, is asking for help in developing an essay on game theory and international conflict: particularly, that Israel and Palestine:
“Israel and Palestine and game theory I have been writing an article for the journal Public Choice on conflict in the Middle East. I am no Middle East scholar, or close to it, but I was asked to consider, from the point of view of game theory, how persistent international conflict might be possible. The Coase Theorem, after all, that touchstone of law and economics, tells us that parties will strike a mutually beneficial deal. But they don’t, so why not?
Can you give a rational choice account, in ten words or less, why the two parties don’t cut a deal?”

Well, I don’t work well with word count limits, but here goes:
Because there are more than two parties with conflicting interests.
(Ten exactly! See, I can write to spec. Now somebody start paying me.)
Game theory is hardly my area of expertise, so stop me if I start sounding stupid. But it seems to me that any attempt to comprehend the “Israeli- Palestinian” conflict that begins by assuming that there are only two sides in the conflict is doomed to failure.
The Israeli side has a wide spectrum of political parties jousting for power, each with its own view of how relations with the Palestinians should proceed. And on the Palestinian side, the divisions between the PLO leadership of Prime Minister Abbas and the ambitions of Hamas are well known. (Not to mention the equally clear split between Abbas’ faction and Arafat’s).
And we see how this applies to wrecking the game theory model on a regular basis. We’ve all grown used to the pattern: the moderate factions on each side agree to a negotiated peace deal. Then Hamas (or a PLO faction) escalates the violence, derailing the negotiation process.
And here’s another thought for you: Why should we conclude that the current state of unending violence and conflict is not necessarily what some terrorist groups such as Hamas actually want? And keep in mind, that’s not the same thing as saying that every single individual Hamas member wants unending war: Hamas as an institution, I think it can be argued, is designed to perpetuate violence and conflict. It’s not built for making peace — if you actually did ever manage to make peace with it, it would have ceased to be Hamas.
(And by the way: another problem is that if you take the stated goal of Hamas’s charter seriously, it’s the destruction of the state of Israel. So it’s fairly easy to see why there’s no possibility of compromise with the Israeli side; there is no mutually beneficial solution if that’s their starting point.)
So to wrap up from the game theory perspective:
1) If you want to properly apply it in this case, you can’t just use a simple two-player model, it has to be something far more complex with far more players.
2) Some of the players have mutually incompatible goals (Hamas: Destroy Israel; Israel: Avoid being destroyed)
Now I’ve gone way over ten words. But I suspect the subject deserves far more…