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Peace Now, or Never

http://www.nytimes.com/2011/09/22/opinion/Olmert-peace-now-or-never.html?_r=1&hp

The tension between Palestine and Israel is heightening as Palestine is trying to get recognized as a nation-state in front of the United Nations General Assembly (UNGA). Many scholars including Mr. Olmert, 12th Prime Minister of Israel, advocates a two-state solution. Under the two-states solution, “the territorial dispute would be solved by establishing a Palestinian state on territory equivalent in size to the pre-1967 West Bank and Gaza Strip with mutually agreed upon land swaps that take into account the new realities on the ground” (Olmert 2011). In addition, Jerusalem should be shared by both Jews and Arabs and recognized as the capital of both Israel and Palestine. This suggestion is very ideal for both countries, which have decided to pursue peace after decades of bloody fighting. However, the problem is that both counties want more territory and international recognition. The Israeli Prime Minister, Benjamin Netanyahu believes in the two-state solution, but is recently putting his greatest effort to block Mr. Abbas’s bid for statehood in front of UNGA. His plan is to politically contain Mr. Abbas, so Mr. Abbas won’t win any international support. Mr. Abbas as the president of Palestine is trying to win the statehood and international support in order to win a higher ground when he has to negotiate with Mr. Netanyahu over the two-state solution.

The problem with this ongoing and time-consuming power game is that Hamas, highly violent Palestinian military faction from the Gaza Strip, is slowly rising against both Mr. Abbas and Israel. It is a great opportunity for Israelis that Mr. Abbas is leading Palestine because he is one of the few Palestinian leaders, who object to terrorism, Hamas, and want peace. Furthermore, many Israelis are becoming more skeptical about a peaceful negotiation with Palestine. “In the worst-case scenario, chaos and violence could erupt, making the possibility of an agreement even more distant, if not impossible” (Olmert 2011). The time is running out and both leaders must abandon the power game and make a decision.

The 2 x 2 ordinal games is created to help Mr. Abbas, representing Palestine, and Mr. Netanyahu, representing Israel, in making the right decision for both countries’ future. This particular game is based on the 2 x 2 ordinal games known as Chicken. The game of chicken is named after an imaginary “sport” in which opposing drivers maintain a head-on collision course until at least one of them swerves out of the way. The one who swerves first loses and ties can also occur; both drivers can either swerve or collide. There are four possibilities in this particular game. “4” represents the most preferred possibility and “1” represents the least preferred possibility for both countries.

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(N,N) or (3,3) represents both parties’ mutual negotiation via diplomacy or peace talk. (N,DN) or (2,4) represents the situation when Palestine attacks Israel, while Israel is trying to negotiate. (DN,N) or (4,2) represents the situation when Israel attacks Palestine, while Palestine is trying to negotiate. (DN,DN) or (1,1) represents the total war between Israel and Palestine caused by both parties’ denial of negotiation.

It is clear that the worst case scenario for both country is (1,1) when each country unilaterally chooses DN over N. In this particular game, neither Row nor Column has a dominant strategy, but both (4,2) and (2,4) are the pure strategy Nash equilibria. A dominant Strategy occurs when one strategy is better than another strategy for one player, no matter how that player’s opponents may play. To prove that there is no dominant strategy, I am going to start off by proving that N is not a dominant strategy for Israel. To do this, I need to produce a scenario in which DN produces a better result for Israel than does N. When Palestine chooses N, a choice of DN by Israel yields (4,2), while a choice of N by Israel yields (3,3); 4 is greater than 2. Hence, N is not a dominant strategy for Israel. DN is also not a dominant strategy for Israel. When Palestine chooses DN, a choice of N produces a better result for Israel than does DN. When Palestine chooses DN, a choice of N by Israel yields (2,4), while a choice of DN by Israel yields (1,1); 2 is greater than 2. For similar reasoning neither N nor DN is a dominant strategy for Palestine.

Suppose that Israel chooses a strategy N and Palestine chooses a strategy DN. We say that this pair of strategies (N, DN) is a Nash equilibrium if N is a best response to DN, and DN is a best response to N. Also, suppose that Israel chooses a strategy DN and Palestine choose strategy N. We say this pair of strategies (DN, N) is a Nash equilibrium if DN is a best response to N, and N is a best response DN.
For Israel: If Palestine chooses DN then Israel’s best response is N because N = 2 is better than when DN = 1. If Palestine chooses N then Israel’s best response is DN because DN = 4 is better than N = 3.
For Palestine: If Israel chooses N then Palestine’s best response is DN because DN = 4 is better than N = 3. If Israel chooses DN then Palestine’s best response is N because N = 2 is better than when DN = 1.
As it is shown, two pairs of strategies (N,DN) = (2,4) and (DN,N) = (4,2) are pure strategy Nash equilbiria.

Now, it is time to analyze the game. We learned three facts by simulating the game. First, there is no dominant strategy for both countries. Secondly, each country’s best response to the other country’s choosing of strategy DN is choosing N. However, it is risky and dangerous because if both countries think in the same manner and decide to use the military power over diplomacy, then (DN,DN),  (1,1), or the full breakout of war might occur. This leads to my final point. (1,1) is the worst outcome because both countries will suffer from the war; everything will be destroyed. Since choosing a strategy DN and hoping the other country to choose a strategy N is highly risky in real world politics, it is wise to avoid going for Nash equilibria. Furthermore (1,1) is not even an option to consider, the only logical choice left is (3,3), which is a mutual negotiation. Thus, it is wise for Mr. Abbas and Mr. Netanyahu to work on the two-states solution advocated by Mr. Olmert.

by SBK64

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