Israel's Conflict as Game Theory
By Prof. Yisrael Aumann
Nobel Prize Laureate
Two men-let us call them Rick and Steve- are put in a small room containing
a suitcase filled with bills totaling $100,000. The owner of the suitcase
announces the following:"I will give you the money in the suitcase under one
condition:you have to negotiate an agreement on how to divide it. That is
the only way I will agree to give you the money."
Rick is a rational person and realizes the golden opportunity that has
fallen his way. He turns to Steve with the obvious suggestion: "You take
half and I'll take half, that way each of us will have $50,000."
To his surprise, Steve frowns at him and says, in a tone that leaves no room
for doubt: "Look here, I don't know what your plans are for the money, but I
don't intend to leave this room with less than $90,000. If you accept that,
fine. If not, we can both go home without any of the money."
Rick can hardly believe his ears. "What has happened to Steve" he asks
himself. "Why should he get 90% of the money and I just 10%?" He decides to
try to convince Steve to accept his view. "Let's be logical," he urges him,
"We are in the same situation, we both want the money. Let's divide the
money equally and both of us will profit."
Steve, however, doesn't seem perturbed by his friend's logic. He listens
attentively, but when Rick is finished he says, even more emphatically than
before: "90-10 or nothing. That is my last offer."
Rick's face turns red with anger. He is about to punch Steve in the nose,
but he steps back. He realizes that Steve is not going to relent, and that
the only way he can leave the room with any money is to give in to him. He
straightens his clothes, takes $10,000 from the suitcase, shakes Steve's
hand and leaves the room humiliated.
This case is called 'The Blackmailer's Paradox" in game theory. The paradox
is that Rick the rational is forced to behave irrationally by definition, in
order to achieve maximum results in the face of the situation that has
evolved. What brings about this bizarre outcome is the fact Steve is sure of
himself and doesn't flinch when making his exorbitant demand. This convinces
Rick that he must give in so as to make the best of the situation.
The Arab-Israeli Conflict
The relationship between Israel and the Arab countries is conducted along
the lines of this paradox. At each stage of negotiation, the Arabs present
impossible, unacceptable starting positions. They act sure of themselves and
as if they totally believe in what they are asking for, and make it clear to
Israel that there is no chance of their backing down.
Invariably, Israel agrees to their blackmailing demands because otherwise
she will leave the room empty handed. The most blatant example of this is
the negotiations with Syria that have been taking place with different
levels of negotiators for years. The Syrians made sure that it was clear
from the beginning that they would not compromise on one millimeter of the
The Israeli side, eager to have a peace agreement with Syria, internalized
the Syrian position so well, that the Israeli public is sure that the
starting point for future negotiations with Syria has to include complete
withdrawal from the Golan Heights, this despite its critical strategic
importance in ensuring secure borders for Israel.
The Losing Solution
According to game theory, Israel has to change certain basic perceptions in
order to improve her chances in the negotiations game with the Arabs and win
the long term political struggle:
a. Willingness to forego agreements
Israel's political stand is based on the principle that agreements must be
reached with the Arabs at any price, that the lack of agreements is
untenable. In the Blackmailer's Paradox, Rick's behavior is the result of
his feeling that he must leave the room with some money, no matter how
little. Because Rick cannot imagine himself leaving the room with empty
hands, he is easy prey for Steve, and ends up leaving with a certain amount
of money, but in the role of the humiliated loser. This is similar to the
way Israel handles negotiations, her mental state making her unable to
reject suggestions that do not advance her interests.
b. Taking repetition into account
Game theory relates to onetime situations differently than to situations
that repeat themselves. A situation that repeats itself over any length of
time, creates, paradoxically, strategic parity that leads to cooperation
between the opposing sides. This cooperation occurs when both sides realize
that the game is going to repeat itself, and that since they must weigh the
influence present moves will have on future games, there is a balancing
factor at play.
Rick saw his problem as a onetime event, and behaved accordingly. Had he
told Steve instead that he would not forego the amount he deserves even if
he sustains a total loss, he would have changed the game results for an
indefinite period. It is probably true that he would still have left the
game empty handed, but at the next meeting with Steve, the latter would
remember Rick's original suggestion and would try to reach a compromise.
That is how Israel has to behave, looking at the long term in order to
improve her position in future negotiations, even if it means continuing a
state of war and fore going an agreement.
c. Faith in your opinions
Another element that crates the "Blackmailer's Paradox" is the unwavering
belief of one side in its opinion. Steve exemplifies that. This faith gives
a contender inner confidence in his cause at the start and eventually
convinces his rival as well. The result is that the opposing side wants to
reach an agreement, even at the expense of irrational surrender that is
considerably distanced from his opening position.
Several years ago, I spoke to a senior officer who claimed that Israel must
withdraw from the Golan Heights in the framework of a peace treaty, because
the Golan is holy land to the Syrians and they will never give it up. I
explained to him that first the Syrians convinced themselves that the Golan
is holy land to them, and then proceeded to convince you as well. The
Syrians' unflinching belief that they are in the right convinces us to give
in to their dictates. The only solution to that is for us to believe
unwaveringly in the righteousness of our cause. Only complete faith in our
demands can succeed in convincing our Syrian opponent to take our opinion
As in all of science, game theory does not take sides in moral and value
judgments. It analyzes strategically the behavior of opposing sides in a
game they play against one another. The State of Israel is in the midst of
one such game opposite its enemies. As in every game, the Arab-Israeli game
involves interests that create the framework of the game and its rules.
Sadly, Israel ignores the basic principles of game theory. If Israel would
be wise enough to behave according to those principles, her political status
and de facto, her security status, would improve substantially.
Copyright Yisrael Aumann