Today’s online edition of the Israeli newspaper Haaretz features an op-ed by the journalist Ari Shavit (I actually know him personally, but of course all Israelis know each other). Its title is “Game theory and the bomb”. Which bomb? The hypothetical Iranian nuclear bomb. Shavit summarizes a discussion with the retired general Yitzhak Ben Israel. The latter observed that an Israeli military strike against Iran may speed up rather than slow down the development of the Iranian nuclear arsenal. His argument is that after the strike, the fear of bringing about a military strike will no longer hold the Iranians back. Of course a strike may also be successful in delaying the bomb, but its outcome is uncertain.
The crucial paragraph, which gives the article its name, is puzzling. It loosely translates as follows:
“No one … can predict the outcome of action or inaction. But when there is uncertainty, the guiding principle should be the one defined by the father of game theory, John von Neumann. The Jewish mathematician, who was one of the leaders of the Manhattan project, argued that in critical situations where you do not know the outcome, you should not maximize benefit but rather minimize loss in case of failure. If a strike hastens the bomb then Israel would pay the maximum price. Therefore, via mathematical analysis, Israel must choose to avoid a strike.”
QED. I found it amusing that Shavit points out that von Neumann was Jewish, as if that makes him uniquely qualified to save the Jewish state via his mathematical insights. More importantly, this has got to be the most informal “mathematical analysis” I have ever seen. It also seems fundamentally flawed. von Neumann’s Maxmin strategies deal, in a sense, with uncertainty about the other player’s intentions, and therefore work under the assumption that the other player plays adversarially (the game may not be zero-sum). It seems that Shavit, and presumably Ben Israel, are confusing this type of uncertainty with the uncertainty that comes from a move by nature (throwing dice to determine the outcome of a strike).
Any ideas on how to formalize Shavit’s argument, or whether it makes any sense at all, for that matter? To give you a bit of incentive, the first successful solution will receive the Nobel peace prize.