Game Theory in the Middle East

One way to approach understanding what is necessary to achieve peace in an ongoing conflict, such as the conflict in the Middle East, is to view the conflict as a game. Dr. Robert Aumann, in his Nobel lecture about Game Theory, stressed that in order to apply Game Theory to the study of conflict one has to make the assumption that the players are making rational choices. That is a highly questionable assumption when it comes to the Middle East; nevertheless viewing the conflict in the Middle East as a game can make clear just how irrational the choices of the players are. Game Theory also can predict non-intuitive and paradoxical results to policies which as we shall see apply to the Middle East.

If we are going to model the Middle East conflict as a game the first question we need to answer is who are the players in the Middle East? The main players are Israel and the Palestinian Authority and Hamas, but the United States influences Israeli policy and the Saudis influence U.S. policy. Arms and training from Iran are what made possible the defeat of Israel by Hezbollah in Lebanon and Iran is doing the same for Hamas. Russia has been arming Syria and Iran with state-of-the-art anti-aircraft missile defense systems.

The second question we need to answer is what are the goals of the players? If the primary goals of both Israel and the Palestinian Authority was peace there would be peace; you don’t need Game Theory to tell you that. Likewise you don’t need Game Theory to know that if one party wants peace and the other doesn’t, there won’t be peace. So if the primary goals are not peace what are they?

The Palestinian Authority’s goals: We can learn the goals of the Palestinian Authority from murderous Sheikh Mudeiris, who on Palestinian Authority Television said (Bogdanor, 2008):

. . . the Jews are a virus resembling AIDS, from which the entire world suffers . . . the Jews were behind all the civil strife in this world. The Jews are behind the suffering of the nations . . . The day will come when we will rule Britain and the entire world – except for the Jews. The Jews will not enjoy a life of tranquility under our rule, because they are treacherous by nature, as they have been throughout history . . . The stones and trees will want the Muslims to finish off every Jew.

We can learn the goals of the Palestinian Authority from the maps of Palestine in 3rd-grade textbooks that are missing Israel (Jewish Virtual Library, 2008). True, Palestinian Authority Chairman Abbas states to Western leaders that he wants peace, but as we shall see later that is the strategically correct move to make in order to weaken Israel. Although Abbas makes peaceful statements to the U.S., Abbas’s statements to his Palestinian brethen are anything but peaceful. Abbas reportedly financed the massacre of Israeli athletes at the Munich Olympics. He even kissed Mohammed Daoud, the organizer of the attacks, and wished him luck. The very same day that an Islamic Jihad suicide bomber killed at least five Israelis and wounded more than 40 innocent people in a Netanya shopping mall, the Palestinian daily, al Hayat al Jadida, reported that Abbas signed a new law to support the families of suicide bombers. He encouraged young students in Gaza to be martyrs by telling them that violence was the reason the Israelis withdrew from Gaza and by telling them that, “[Martyrs] receive their reward in the Garden of Eden.”

After Hezbollah fired Katyusha rockets that killed eleven Israelis, Abbas praised Hezbollah, telling reporters that the Hezbollah war has re-awakened the Arab world with honor and is an example for others to follow (Isaac 2006). In an interview with the Jordanian daily Al-Dustur (translated by Marcus and Crook, 2008), Abbas said that he was "honored" to have fired the first bullet of the Fatah terror organization in 1965, and to have taught terror tactics around the world, including to such groups as Hizbullah. He explained to the interviewer that the PA is "unable" to pursue armed conflict for now, but said that "in the future stages things may be different." He rejected Israel as a Jewish state, and boasted that it was the PA's rejection of Israel's Jewishness that almost aborted the Annapolis Conference last November. He also said that he won't demand that Hamas recognize Israel. In fact, Palestinian Media Watch has reported that he said that the only "recognition" of Israel he demands of a Palestinian unity government is to recognize Israel as its adversary.

The Bush Administration claims that not only Abbas but the Palestinian people are peaceful (Isaac 2006), but recent polls show that 85% of Palestinian Authority Arabs support terror and of the 15% who don’t, an undetermined number have strategic and not peaceful reasons for not supporting terrorism against Israel. (HaLevi 2008c).

Israel’s goals: In contrast to the extremist rhetoric of the so-called moderate peace-loving Palestinian Authority, the former leader of the so-called hardline right-wing Likud Party of Israel, Benjamin Netanyahu, explained to the U.S. Congress in 1996 that:

Our hand is stretched in peace to all who would grasp it. We don't care about their religion. We don't care about their national identity. We don't care about their ideological belief. We care about peace, and our hand is stretched out to peace.

Every Israeli wants peace. I don't think there is a people who has yearned, prayed and sacrificed more for peace than we have. There is not a family in Israel that has not suffered the unbearable agony of war and, directly or indirectly, the excruciating, ever-lasting pain of grief. The mandate we have received from the people of Israel is to continue the search for an end to wars and an end to grief. I promise you: We are going to live up to this mandate. We will continue the quest for peace, and, to this end, we are ready to resume negotiations with the Palestinian Authority on the implementation of our Interim Agreement.

Hamas’s Goals: Addressing a mass rally in memory of the founder of the Hamas terrorist organization, Ahmed Yassin, senior Hamas leader and former Palestinian Authority official Mahmoud A-Zahar reiterated that the goal of Hamas is the complete obliteration of Israel and the worldwide rule of Islam (Nissan Ratzlav-Katz 2008).

Hezbollah’s Goals: Hezbollah head Hassan Nasrallah said that “the destruction of Israel and the liberation of Palestine and Jerusalem are “the principal objective of Hezbollah." (Passner 2006) Hezbollah has other goals too. He said on Al-Manar:

Let the entire world hear me. Our hostility to the Great Satan [America] is absolute . . . I conclude my speech with the slogan that will continue to reverberate on all occasions so that nobody will think that we have weakened. Regardless of how the world has changed after 11 September, Death to America will remain our reverberating and powerful slogan: Death to America.
– BBC Monitoring: Al-Manar
, Sep. 27, 2002.

Iran’s Goals: Ahmedinejad has made Iran’s goals clear with statements such as, "The countdown has begun for the destruction of Israel" (Marcus, 2008) and in his statement to a huge crowd in Teheran that, "Is it possible for us to witness a world without America and Zionism? But you should know that this slogan and this goal are achievable, and certainly can be achieved." The crowd responded with the popular Islamic chant, "Death to America!" One dramatic example of this can be seen on MEMRITV (2007).

Russia’s Goals: Russia wants, at a minimum, to contain American power. Russia, by arming Iran with the Tor M1 and S300 missile defense systems, has made destroying Iran’s nuclear sites from the air a very costly proposition. Russia has sold these missile defense systems to Syria as well. These defense systems could make it impossible for Israel to launch effective retaliation if Syria bombards Israeli civilians with its rapidly growing arsenal of rockets and thus make it more likely that Syria will attack Israel.

The Goals of the United States: The United States wants to please the Saudis in order to keep the oil and oil money flowing. (Pipes 2002) The United States wants to curry favor with as much of the Arab world as possible. The United States also wants to minimize antagonism from the Arab world arising from U.S. support for Israel. That much is obvious, the rest is murky. The reason the rest is murky is because American policy in the region has been so counterproductive to the Bush administration's stated commitment to Israel’s security. Condoleezza Rice keeps demanding dangerous concessions from Israel (Ronen 2008) and despite their terrible consequences (Knish 2008) keeps demanding more. If we choose to believe the statements of the Bush administration, then its two primary goals are 1) to bring peace to the Israelis and the Palestinians before the Bush presidency is over, and 2) to stop Iran from acquiring nuclear weapons.

Are the Players Making the Right Moves?

Russia is making money off of weapons sales and shifting the balance of power against Israel and the United States. However, protecting the Iranian nuclear program by selling Iran anti-aircraft missile systems is a very dangerous move on Russia’s part. The weapons used today against the Israeli and American infidels are likely to be used against the infidels of Russia tomorrow, especially when we consider that Russia has already suffered terrorist attacks from Muslims and that the Muslim Chechens are unlikely to forget the way Russia leveled Grozny.

Saudi Arabia charges the United States exhorbitant prices for oil and uses that money to spread Wahabism and fund Jihad. (Simpson, 2007) U.S. appeasement policies toward Saudi Arabia have not changed that.

Both Israel and the United States want peace now and whatever concessions Israel is reluctant to make, the United States is willing to pressure it into making so that there will be peace now. Game Theory shows that doing this leads to war, not peace. Robert Aumann explained this paradox as follows (2007):

If you insist on peace now you may never get peace but if you are willing to wait than you may get peace now.

We can understand this if we imagine ourselves playing a chess game with an opponent who has more pieces than we have but desperately wants peace. Let's say our opponent offers us a deal: if we are willing to make peace he will let us take his most valuable piece, his queen. Our goal is to checkmate our opponent, not to make peace with him, but if we don’t accept his offer we know we won’t win the game. So we do accept his offer, he sacrifices his queen and then we betray our agreement and continue to take his pieces.

That is analogous to what the Palestinians did with the Oslo agreement: they promised peace in return for Israeli concessions and then continued to be violent. If your opponent is incredibly stupid he may offer you his knights to create goodwill and jump-start the peace process. This is analogous to Israel giving the Palestinian Arabs Gaza even after the Oslo betrayal. After you take his knights you might as well continue to demand more pieces. Why not demand that he give up his castles and that he allow your queen to move close to his king. He will have no reason to do this if there is peace, so you have to keep attacking him.

This is analogous to the demands of the Palestinian Authority that Israel give them all of Judea and Samaria and allow for the right of return of the Palestinian refugees while they continue to commit terrorist attacks against Israel. Your opponent may be reluctant to let you put your queen close to his king (the right of return) but he might offer you his castles as part of the peace process. This is analogous to the willingness of Prime Minister Olmert to give Judea and Samaria to the Palestinian Authority so that the peace process will continue. Note that this time, you are not even pretending that your opponent will have peace if he sacrifices his castles; you have made it clear that he has to sacrifice his castles and allow your queen close to his king, but he sacrifices his castles anyway to keep the peace process going.

An important lesson from this chess game is that it is in your interest to keep attacking so that the opponent keeps sacrificing pieces for peace. Israeli offers of concessions for peace is a strong incentive for making war.

It is hard to believe that any opponent would be as stupid and irrational as to make the moves that I have described in the chess game, but that is exactly what Israel has done.

In 1996, Benjamin Netanyahu displayed a rational grasp of the ongoing game in the Middle East when he explained to the U.S. Congress that,

Those governments that pursue peace at any price pay a very high price indeed and do not get peace.

and that:

We bargain, and the Arabs collect.

Unfortunately, after his speech Netanyahu proceded to act irrationally and bargain further. (Shapiro 2007)

What are the right moves for the United States and Israel to make to win the peace? To find an answer to this question we will consider what Dr. Aumann said in a speech in which he explained some of the concepts of Game Theory in layman’s terms. (Aumann, 2007) Here is an excerpt from that speech.

Suppose someone comes to your door and wants to sell you something and suppose that he doesn’t come from a company that you ever heard of. He does not come from a reputable company. You’ll think twice about buying the merchandise he’s selling you. Why? Well, because it’s clear that you’ll never see him again. What happens if he sells you shoddy merchandise, you have no place to go. But if there is somebody that has a store in your neighborhood, you’ve seen him before, you’ll see him again. You’ll buy from him because he wants to do business with you tomorrow as well and he did business with you yesterday and he knows that when he sells you shoddy merchandise than you will not come back to him. It’s as simple as that. You have an incentive to cooperate with him and he has an incentive to cooperate with you.

And what is creating those incentives is something that doesn’t sound very nice but it’s God’s honest truth. What is creating the cooperation is the threat of punishment, that you won’t go to him again. He’s not going to sell you shoddy merchandise if you have a long term interaction. If he’s around, if he’s identifiable, if he opens a store. What’s creating the cooperation is the threat of punishment; it doesn’t sound nice but that’s how it is.

When the threat of punishment is removed, conflict increases. One of the problems of Western society, for example, is that out of misguided compassion for children, there are extensive restrictions on punishing them when they misbehave. The result is very disrespectful and badly behaved children compared to those of countries in which parents and teachers can punish misbehavior. The schools in Hackney England, for example, have children who are more badly behaved than those of Mitchell's Plain (in the bleak, infamous, gang-ridden Cape Flats) of South Africa, according to African teachers who have taught in both places. Why? Because in England if a teacher so much as touches a pupil he or she can be charged with abuse. (Braid, 2001)

The result of this misguided compassion is that the children become victims of violent abuse from each other, and the schools become unable to hire enough teachers willing to endure abuse from the students. This policy was created by people who did not understand the need for punishment. What applies to the children of Hackney also applies to adults. Robert Aumann pointed out that:

in the long years of the cold war between the United States and the Soviet Union what prevented hot war was that bombers carrying nuclear weapons were in the air 24 hours a day, 365 days a year.

It was fear of nuclear punishment that kept Russian and American adults from killing each other.

If we go back to the chess game analogy, the way for our opponent to make us peaceful is to threaten to checkmate us if we attempt to take any of his pieces. If he is more powerful than we are, we had better comply.

Mahmoud Abbas and his predecessor, Yassir Arafat, have played the game so well that the United States and the Western world are helping him achieve his goal of annihilating Israel. Just as in the chess game example I gave before, it is in Abbas’s interest that Israel keeps being attacked so that Israel keeps making sacrifices for peace. The problem Abbas faces is that he has to keep the hope of peace alive while Israel is being attacked, so that Israel will keep making concessions. He can do this by arguing that he is for peace, but that he needs more arms to control and defeat the violent Palestinians. The Saudi-pleasing U.S. is all to happy to comply and is currently financing, training and arming Abbas’s terrorists so that they will fight Hamas terrorists. (Klein 2008) Abbas and Arafat have convinced the United States that the only way peace can be achieved is for Israel to uproot Israelis from their homes. This paves the way for civil war and shrinks Israel to a more conquerable size.

Dr. Aumann said in regard to the uprooting of the Israeli inhabitants of Gaza that it was:

an unprecedented act of barbarism, self-hatred and stupidity . . . There is only one way to achieve peace in the Middle East and that is to convince our Arab cousins that we are not the Crusaders. We are here to stay. They must be convinced that we will not move . . . They see that violence pays, that it pays off. They are not punished, they are rewarded. Gaza today, the West Bank tomorrow, Haifa, Yaffo, Tel Aviv thereafter.
– (Chesler, P. 2006)

Events proved Dr. Aumann’s analysis correct. Uprooting Israelis from Gaza did not bring peace; instead, the beautiful tree-lined paradise the Israelis created in Gaza has become a desert launching pad for rockets against Israeli civilians in Sderot and Ashkelon and against the Israelis who were uprooted from their homes.

Israel and the United States — partly out of desperation to avoid casualties — are making the wrong moves. Israel doesn’t want to lose the lives of its own soldiers and does not want to kill civilians on the other side either. The United States is courting the Arab world and the last thing it wants is the Arab world to become enraged at the United States because of casualties from conflict with Israel. The problem with a policy based on casualty avoidance is that in the end it results in more casualties and more conflict. Ralph Peters has written:

A policy of casualty aversion – in Israel or in the United States – results in more casualties in the end.
– (Peters, 2006)

Dr. Aumann also made this argument. He said:

The main preparation for war has to be an emotional preparation. It has to be in your head. You have to be prepared for losses, you have to be prepared for your men getting killed and you have to be prepared for the enemy’s people getting killed also. We’re prepared for neither one. When 25 Arabs get killed our television is up in arms but we’re also not prepared for our own men being killed. One of the main problems of the second Lebanon war last summer was that we did not want to go in with ground troops. Why? Because going in with ground troops mean that you may get killed, you don’t want to get killed but you can’t fight a war without getting killed. War is a bloody business, I’m sorry. If you don’t want to get killed you have to be ready to get killed, that is what will prevent your getting killed and prevent you from having to go to war at all. If you’re ready to get killed and ready to kill. These things sound very unpleasant but war is unpleasant. We are in a very unpleasant situation. We are in a war that has lasted for 80 years. It’s not last summer’s war and it’s not the peace for Galilee operation, these are just battles in the war. This war has lasted 80 years. This war is going to continue until we are ready to face it; when we are ready to face it and sell our Arab cousins on the proposition that we are intending to stay here, then we may get peace, and that, Ladies and Gentlemen, is Game Theory in the Middle East.

The Bush administration — which knows better than to micromanage the war in Iraq — micromanages Israel’s military to make sure there are minimal Arab casualties. Mark Silverberg wrote about the disastrous consequences of this micromanagement in an article titled "Lessons from Lebanon." (Silverberg, 2008) He wrote:

Both President Bush and Secretary of State Rice agreed to back Olmert’s air campaign plan provided that Olmert received prior American approval for a ground offensive – which came only after weeks had passed and only after the air war had proven to be ineffective and, some would argue, even counter-productive. This explains why Israel’s land invasion was delayed for three weeks and why the IDF was required to remain on their bases instead of engaging in battle. When that decision finally came, it was with another stipulation that Israeli forces were not to advance to the Litani River. Again, Washington demanded a halt to the advance. By the time the final decision was made to carry out the Litani operation and to vanquish Hezbollah, it was too late. The ceasefire was effectively a foregone conclusion.

DEBKA sources note: “This last disastrous order released the welter of conflicting, incomprehensible orders which stirred up the entire chain of command – from the heads of the IDF’s Northern Command down to the officers in the field. Operational orders designed to meet tactical combat situations were scrapped in mid-execution and new directives tumbled down the chute from above. Soldiers later complained that in one day, they were jerked into unreasoned actions by four to six contrary instructions.” The problem with these contradictory directives was that none of the commanders at any level (including the Chief of Staff) could explain what was happening since they had not been privy to any of the “backroom decision-making” in the Prime Minister’s office.

But it didn’t end there. Olmert had also promised Bush and Rice to spare Lebanon’s civilian infrastructure and direct his air campaign to Hezbollah’s positions and installations. As a result, Israeli forces were not initially allowed to destroy buildings known to be occupied by Hezbollah teams firing anti-tank missiles because it would have meant destroying Lebanese infrastructure. This decision resulted in a dramatic increase in Israeli casualties as the IDF was required to return again and again to cleanse terrorist bases in Maroun a-Ras, Bint Jubeil and Atia a-Chaab.

Taking all this into account, Olmert’s absolute compliance with Rice’s directives threw Israel’s entire war campaign into disorder. Supply trucks could not locate various units that were left without food and water, the subject of one of the bitterest complaints . . .

The disastrous result of casualty and infrastructure avoidance is that Hezbollah is still intact and stronger than ever. According to Debkafile (2008):

Hizballah has built up its rocket arsenal to three-and-a-half times its pre-2006 Lebanon War stocks. Some of the 40,000 rockets of Syrian and Iranian manufacture can hit Israel targets as far south as Beersheba, 350 km away from the Shiite terror group’s launching pads north of Lebanon’s Litani River.

Not only has Tel Aviv come within range, but Hizballah and the Palestinian Hamas in Gaza can between them cover most of Israel except for its southernmost tip at Eilat . . . DEBKAfile’s military sources report the lion’s share of rockets smuggled to Hizballah in recent months are Syrian-made. Damascus has also shipped to Hizballah quantities of anti-air weapons, including shoulder-borne rockets and scores of Russian-made anti-aircraft ZSU-100 automatic 14.4 mm caliber cannon, which are most effective against low-flying aircraft, helicopters and drones.

The day will come when Hezbollah will launch another massive attack against Israeli civilians from Lebanese civilians areas. Clearly 40,000 rockets will kill more Israeli civilians than were killed during the last Hezbollah-Israeli war. Israel will be forced to attempt to stop the rockets and as a result many more Lebanese civilians will die. This is an example of how policy based on casualty avoidance leads to more casualties.

The argument has been made that Israel should not have gone to war with Hezbollah to begin with since the number of people who died in the war was greater than the number killed by Hezbollah in the incident that ignited the war. This neglects the fact that if terrorism violence is ignored it continues and that it increases as well. It also ignores the fact that the longer you wait to retaliate against terrorism the more powerful the terrorists will be and the more casualties you and the civilians among whom they are based will suffer. This is shown graphically in the appendix to this article.

The greatest threat to Israel and for that matter the United States is a nuclear Iran. The United States does not strike Iran because of fear of casualties, yet the casualties the U.S. will experience if Iran is not stopped are unimaginable.

The only incentive that would have stopped the Iranian government from building nuclear weapons is fear that the United States would overthrow them the way they overthrew Saddam. Instead, the United States along with the Europeans, attempts to appease Iran. Game theorists have demonstrated the dangers of appeasement (Milgrom and Roberts. 1982 and Kreps and Wilson. 1982), as has the history of World War II.

While the U.S. waited for European attempts to appease Iran to bear fruit, the Iranians deployed the Russian Tor M1 air defense system, a system with an aircraft kill probability of over 90% for aircraft flying up to 18,000 feet and 7 miles away. As the United States continues to wait for peace to break out, the Iranians and the Syrians are deploying the Russian S-300 anti-aircraft missile defense system which is capable of shooting down aircraft, cruise missiles and ballistic missile warheads at ranges of over 90 miles and at altitudes of about 90,000 feet. While the United States patiently does nothing, the Iranians enrich uranium and test rockets that can carry nuclear weapons. The number of casualties that the U.S. suffers today from Iran is nothing compared to what it will suffer in the future if Iran is not stopped and the cost of defeating Iran rises each day.

What Moves Should the Players be Making?

If fear of punishment is what is necessary to keep the peace, we need to ask what fear would keep the peace. Just as mutually assured destruction doesn’t deter a suicide bomber, it might not deter Iran. That is one reason why it is so important to destroy their nuclear program.

The primary goal of the Palestinian Arabs is the destruction of Israel; if they see that violence actually brings them further from that goal that will motivate them to act peacefully. If they know that Israel will retaliate to any acts of violence by annexing land and they know that the world will support Israel in doing so, the Palestinian Arabs will have a strong incentive to refrain from terrorism. Of course, this is an inversion of reality; the world automatically condemns any effort of Israel to defend itself and the United States — in order to avoid antagonizing the Arabs — does not allow Israel to return to the lands they gave up for peace. The United States also makes sure that any Israeli retaliation is minimal, which makes it impossible for Israel to stop the rocket attacks at Israeli civilians. The inability of Israel to stop rocket attacks against it sends the lethal message that Israel is weak and that the time for Israel’s annihilation is close at hand. The United States — in its efforts to prevent conflict — is bringing on that conflict.

Palestinian leaders have another motivation besides destroying Israel and that is staying in power and channeling Western aid into their own pockets. If attacks on Israel were to be met with cuts in Western aid, that too would be a powerful motivating force to refrain from attacks. Not only is this not done, but the United States forces Israel to provide money to the Palestinians in Gaza even when terrorists are shooting rockets at Israel from there.

One doesn’t have to be a brilliant Game Theorist to understand that Israel and the United States are losing the game because of, as Dr. Aumann put it, “unprecedented stupidity.”

* * *

References

Aumann, Robert (2007) Euroshiur: Professor Robert Aumann – Middle Eastern Games.
http://www.youtube.com/watch?v=rJAFRF75OVA

Bogdanor, Paul (2008) Understanding the Arab Israel Conflict.

Braid, Mary (2001) "Don't go and teach British 'monsters,' warn teachers recruited from," The Independent, 8/4.

Chesler, Phyllis (2006) "A Rational War," Frontpage Magazine, 11/18/06.

Debkafile (2008) Exclusive: "Hizballah more than trebles rocket arsenal to 40,000," 3/22.

Fain, David. (2007) "Sderot . . . I Can’t Hide My Ignorance Anymore," 10/8.
http://sderotmedia.com/?cat=12/.

HaLevi, Ezra. (2008) "Ashkelon Katyushas Came From Iran Via Egypt," Israel National
News,
3/14.

HaLevi, Ezra. (2008b) "Ashkelon Shelling Draws Record Day of IAF Air Strikes on Gaza," Israel National News, 3/14.

HaLevi, Ezra. (2008c) "Poll shows 85% of Palestinians Support Terror," Israel National News, 3/14.

Haselkorn Avigdor, "Iran’s Hidden Hand in Gaza," FrontPageMagazine.com, 3/19/2008.

Isaac Gamaliel (2006) "A Glorious Vision: Misconceptions and the Middle East," Intellectual Conservative, 9/25.

Jacoby, Jeff (2005) "The Problem with Mahmoud Abbas," Israel Insider, 3/22.

Jewish Virtual Library (2008), "Palestinian Maps Omitting Israel."

Klein, A. (2008) "Americans Paying Rent for Terrorists?" WorldnetDaily, 3/23.

Knish S. (2008) "Rice as Diplomat Fairy, Fulfils the Terrorist Wish List," 3/30.

Kreps, David and Robert Wilson. 1982. "Reputation and Imperfect Information," Journal of
Economic Theory
27 (2): 253-279.

Marcus, Yoel (2008) "The Goal: Annihilating Israel," Haaretz.com, 3/22.

Marcus, Itamar and Crook, Barbara (2008) "Abbas rejects Jewishness of Israel, doesn't
rule out armed conflict proud to have taught terror to world," Palestinian Media
Watch Bulletin
http://www.pmw.org.il/Bulletins_feb2008.html#b280208

MEMRITV 2007 "Chants in Iran: Death to America the Infidel," Iranian TV, 2/11/07.

Milgrom, Paul and John Roberts. 1982. "Predation, Reputation, and Entry Deterrence," Journal
of Economic Theory
, 27 (2): 280-312.

Netanyahu, B., (1996) Speech by Prime Minister Benjamin Netanyahu to a Joint Session of the United States Congress, 7/10.

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3/22.

Passner, Deborah, 2006 "Hassan Nasrallah in His Own Words," CAMERA, 7/26.

Peters, Ralph, 2006 "Lessons so Far: Hard Lessons to Learn From Israel’s War on Hezbollah," New York Post, 8/13.

Pipes, Daniel (2002) "The Scandal of U.S. Saudi Relations," National Interest, Winter 2002/2003.

Ronen, Gil (2008) "U.S. Very Surprised at Extent of Israeli Concessions," Israel National News, 3/31.

Shapiro, Ben (2007) "Netanyahu’s Back, More of the Same?" Outpost (Newsletter of
Americans For a Safe Israel), 8/28.

Silverberg, Mark (2008) "Lessons from Lebanon," The New Media Journal, 2/6.

Simpson, Glenn, (2007) "U.S. Tracks Saudi Bank Favored by Extremists," The Wall Street Journal, 7/26.

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* * *

Appendix

Let the variable I represent the total number of people who will die if Israel invades Gaza. Let the variable C represent the number of civilians who will die from rocket attacks if Israel does not invade. Those who argue that Israel should not invade argue that:

Equation

We know that the longer Israel waits the more powerful militarily Hamas becomes, and the more soldier’s lives will be lost if Israel finally does invade. The rate at which Hamas military power in Gaza has grown has increased with time, so since the number of casualties is equal to the casualty rate multiplied by time, we can estimate that the number of casualties resulting from invading Gaza goes up as the square of time, or

Equation

Where kI is some constant value and t is time that the Israeli army waits to invade.

Although thousands of rockets have been fired at Sderot and although they have created a terrifying existence for civilians, the number of deaths resulting from these rockets has been low (Fain, David 2007). On the other hand they are increasing. In February 2008 there were two deaths within a week of each other in Sderot. The range, explosive power, accuracy and number of Hamas rockets have increased with time. As a result new cities with larger populations than Sderot are coming into the line of fire. Israel National News reported on March 14, 2008 that waves of Katyusha rockets from Iran were reaching the densely populated city of Ashkelon, (HaLev, Ezra 2008b). We therefore estimate the loss of civilian life as:

Equation

We can learn something from these equations if we plot them. To do that we need to assign values to the constants kNI and kI . We know that about 120 Israeli soldiers died trying to remove Hezbollah from southern Lebanon and the Israeli soldiers didn’t stay long enough to finish the job. Gaza is now better armed than Lebanon was and Hamas now has the benefit of the experience of Hezbollah fighting Israel in Lebanon. I will guess that to succeed in Gaza, now that Hamas is so well armed with anti-tank and anti-aircraft weapons, would be much more costly for Israel and estimate that 400 Israeli soldiers might die. It is difficult to estimate the number of Palestinian civilians who would die since propaganda clouds the accuracy of figures from the Middle East, but I assume that since Hamas is embedded among civilians at least double the number of Palestinian Arab civlians (800) would die if an invasion were carried out today.

In that case:

Equation

Where Itoday is the number of casualties if the invasion were to take place today.

I will also make an educated guess that the current rate of deaths in Sderot and neighboring communities is about 1 a month or 12 a year. In that case:

Equation

We then get the following graph.

Graph

From this graph we see that at some point in time (10 years according to this graph) we reach the point where the number of casualties from not invading begins to exceed the number of casualties if Israel invades now. If Israel waits those 10 years however, the number of casualties the Israeli defense forces would suffer will increase as will the civilian casualties. To graph this we need to calculate ki. The withdrawal from Gaza took place in 2005 which is 3 years ago. If the Israelis had engaged in a military incursion then the casualties would have been only a small fraction of the lives lost when Israel invaded Lebanon. We know this because Hezbollah had a massive bunker system, modern Russian anti-tank weapons and vast numbers of rockets whereas Hamas initially did not. For the purposes of the following approximate calculation we will assume the casualties if the Israelis had invaded Gaza 3 years ago small enough to ignore. In that case:

Equation

We can now graph the number of expected Israeli casualties as a function of time Israel waits to invade Gaza.

Graph

Earlier we saw that after approximately 10 years the number of civilian casualties begins to exceed the number of casualties one would expect if Israel invaded today. The graph above demonstrates that if Israel waits ten years to invade the number of Israeli military casualties as well as Palestinian civilian casualties could be thousands, not hundreds.

The take-home lesson here is that if Israel does not retaliate to terrorist attacks, the casualties due to terrorist attacks will grow until Israel has to retaliate, and then that retaliation will be much more costly in terms of casualties. Retaliation that appears disproportionate in the short term may reduce the number of casualties in the long term.