Multiple choice
Israel's strategy for dealing with Hizbollah has been called "tenfold deterrence": any attack will be met with a far more forceful counterattack. Unfortunately both for Israelis and Lebanese, the strategy did not deter Hizbollah's missiles.
It might seem strange for an economist to offer even these obvious opinions on military strategy, but economists have been armchair generals since the development in the 1940s of game theory by John Von Neumann, a mathematician, and Oskar Morgenstern, an economist. Game theory is the study of situations where each side's actions influence and are influenced by the other side's actions. Since the second world war, game theorists have pondered strategy, deterrence and Armageddon.
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Game theory's power to summarise complex situations in a simple model is sometimes too seductive. The two most overinterpreted ideas in game theory are related to deterrence: the prisoner's dilemma and the strategy sometimes believed to "solve" the dilemma, tit for tat.
The prisoner's dilemma was popularised by a simple story. Two men are captured by the police and separately offered the same plea- bargain: "If you confess and he doesn't, you walk free; if you both confess, you'll both get five years; if neither of you confess, you'll both get one year; if he confesses and you don't, you'll get 20 years." Rational prisoners will confess, wishing there was a way to commit each other to silence. Game theorists have known since the 1950s that when the prisoner's dilemma is repeated indefinitely, more co-operative strategies can flourish. This insight was independently rediscovered and made famous by Robert Axelrod, a political scientist who organised a computerised tournament in which competitors submitted simple programs to play the prisoner's dilemma. The champion was "tit for tat", which begins by co-operating with its fellow prisoner (staying silent) but punishes a squealer by confessing on the next turn. Axelrod argued that "tit for tat" was successful because it was easy to interpret, hard to exploit, began co-operatively and quickly forgave transgressions by returning to co-operation. It has proved a magical myth: that you should speak softly and carry a big stick, that "an eye for an eye" can produce co-operation in unpromising situations. Axelrod's idea was repeated in a horde of popular science books.
But "tit for tat" is just a little too much of a poster child. The repeated prisoner's dilemma is a poor description of real world situations. It didn't describe the cold war, when a nuclear exchange was a one-off game if ever there was one. It doesn't describe the asymmetric struggle between Israel on one hand and multiple decision makers - Lebanon? Hizbollah? - on the other.
Most importantly, the "prisoner's dilemma" is merely a two-player game. Game theorists such as Ken Binmore, a professor at University College London, say this is a crucial omission. Most social arrangements stand or fail with the help of third parties. The crisis in Lebanon will be no exception.
In any case, "tit for tat" is not quite as successful as conventional wisdom would have you believe. A team from Southampton University kicked "tit for tat" off the top spot in a re-run of Axelrod's tournament by entering a collection of team players who colluded with each other. Another successful strategy is "tat for tit", which first tries to exploit the other person and plays nicely only if that doesn't work. Another winning approach is even more depressing, punishing cheats with eternal vengeance. It is known simply as "grim".
“以牙还牙”行不通
以
色列对付黎巴嫩真主党(Hizbollah)的策略被称为“十倍威慑”(tenfold deterrence)：对任何攻击都要报以更为猛烈的反击。对以色列人和黎巴嫩人都很不幸的是，这个策略并未能威慑住真主党的火箭。
如果经济学家提出这种显而易见的军事策略主张，那看起来可能会很奇怪，但自从数学家约翰?冯?诺伊曼(John Von Neumann)和经济学家奥斯卡?摩根斯坦(Oskar Morgenstern)上世纪40年代创立博弈论以来，经济学家们就一直在纸上谈兵。博弈论研究的情形是，其中任一方的行动会影响另一方，同时受到对方行动的影响。自二战以来，博弈论者一直在思考战略、威慑与大决战(Armageddon)。
博弈论能用简单的模型概括复杂的情况，这一能力有时太具诱惑力了。博弈论中，两个过度诠释最严重的观点都和威慑有关：囚徒困境，以及有时被认为能“解决”该困境的策略――“以牙还牙”。
囚徒困境通过一个简单的故事而普及。两个人被警察抓获，警察分别给予两人同样的认罪减刑条件：“如果你招供而他没有，你无罪释放；如果你们两人都招了，两人各判5年；如果都不招，各判1年；如果他招了而你不招，你将判20年。”理性的罪犯都会招供，但都希望存在使对方保持沉默的手段。自50年代起，博弈论者就知道，当囚徒困境无限次重复时，更合作的策略会被普遍采用。这一洞见由政治科学家罗伯特?阿克塞尔罗德(Robert Axelrod)独立地重新发现并使之闻名于世。他组织了一场计算机程序比赛，每位参赛者递交一个简单程序演绎囚徒困境。最后的冠军是“以牙还牙”程序，这个程序始于同被捕的同伴进行合作（也就是保持沉默），但在下一轮则通过招供来惩罚告密者。阿克塞尔罗德指出，“以牙还牙”之所以成功，是因为它易于解释，但难以运用。它始于合作，并且迅速原谅违信行为，重新回到合作。它证明了一个不可思议的荒诞理论：你说话要和气，同时要手持大棒，在前途渺茫的情况下，“以眼还眼”的报复会带来合作。阿克塞尔罗德的观点在诸多科普著作中被反复采用。
但“以牙还牙”有些过于理想化了。以重复的囚徒困境描述真实世界的情形有失偏颇。它无法描述冷战，冷战中核武器交火一旦发生将成为一次性博弈。在以色列与黎巴嫩真主党这场不对称斗争中，它既无法描述以色列的行为，也无法描述另一方多个决策者（黎巴嫩？抑或真主党？）的行为。
最为重要的是，“囚徒困境”只是双方博弈。伦敦大学学院(University College London)教授肯?宾默尔(Ken Binmore)等博弈论者表示，这是个重大疏漏。大多数社会安排的成败离不开第三方的帮助。发生在黎巴嫩的危机也不例外。
在任何情况下，“以牙还牙”都不会像人们通常认为的那样成功。在重新进行阿克塞尔罗德比赛时，来自英国南安普顿大学(Southampton University)的参赛队把“以牙还牙”策略拉下了冠军宝座，他们引入了一个团伙，团伙所有成员事先已串通好。另一个成功的策略是“以牙还眼”(tat for tit)，这个策略首先尝试利用另一方，并只有在这么做不能得逞的情况下才进行合作。还有一个胜出的做法甚至更加令人沮丧，即用不断的报复来惩罚违信者。这就是“恐怖策略”。
