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Game theory and the Blackmailer’s Paradox

By Lachlan Black
web posted September 13, 2021

If someone told you and a stranger that you could share $100,000 if you could agree on splitting it, what would you do? The obvious choice would be to split it 50/50, and everyone would be happy. The stranger then proceeds to say he won’t leave the room with less than $90,000. You end up taking the $10,000 because the stranger won’t back down. Robert J. Aumann presented this “Blackmailer's Paradox” to describe Israel and the Arab countries.

Aumann is an Israeli-American, and a great economist, famous for his game theory. He put forth this idea where two men are put in a room with a suitcase of money. They are told that they could have $100,000 if they could agree on splitting it. One of the men immediately tells the other that he won’t leave the room with less than $90,000. The other man thinks that’s absurd, and tries to talk some sense into him. Aumann explains that the second man eventually caves, and takes $10,000, rather than nothing. Because the stranger remained rational and that he would rather get nothing than $50,000, the other man was forced to behave irrationally, and left the room humiliated.

The Arab and Israel relationship is based on this “Blackmailer's Paradox.” The Arabs put forth absurd and unacceptable starting points. They would act so sure of themselves, making it clear that they wouldn’t back down, and that Israel would be forced to comply. An example of one of the ludicrous negotiations was with Syria. The Syrians told Israel that they would not do any negotiations on “one millimeter” of the Golan Heights. The Israelis of course agreed to this, despite it being of critical importance in ensuring secure borders for Israel, because they were eager for a peace treaty with Syria.

Based on game theory, Israel has to change basic perceptions in order to reach any agreement with the Arab countries. Their political stand is that agreements must be made with Arabs at any cost. The man who received $10,000 in the Blackmailer's Paradox behaved how he did because he was eager to get at least some money, and couldn’t bear to walk away with none. This is similar to Israel, where any rejections of agreements would not help. Game theory studies the ways in which interacting choices produce outcomes.

The “Blackmailer's Paradox” is applicable to the Israel and Arab conflict according to game theory. Robert Aumann concludes that for Israel to retain at least some of her political status, she would need to stop behaving irrationally and put an end to the ridiculous demands of Syria to give up Golan Heights. Syria has complete faith in its position over not giving up Golan Heights, and therefore will not back down. Game theory does not express an opinion over the sides, but seeks to analyze the strategic behaviors of the two parties. If Israel stopped ignoring the principles of game theory, her political status would improve substantially. ESR

This is Lachlan Black’s first contribution to Enter Stage Right. (C) 2021 Lachlan Black

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