I am always wary about applying game theory to real life situations. Plainly we game theorists have many insights about strategic interactions, and our thinking is tuned to strategic analysis, but life is complex, and it is difficult to properly model a given interaction; we often forget to take into acount important aspects that change the whole picture.
An example came up in a recently published interview in an Israeli daily newspaper. Among other things, the interview described a suggestion by a game theorist to solve the problem of missiles shot into Israel from Lebanon and Gaza. According to the interview, the game theorist suggested that Israel builds an automatic machine that, whenever a missile is shot into Israel, waits half an hour and then shoots back a missile; the half an hour is enough time to let the civilians, who live at the place where the first missile was launched from, leave their homes. As we all know from games in extensive form and threat strategies, it is important that the machine is automatic. Such an automatic machine implements a threat strategy, and therefore it should deter deviations.
Let us leave aside moral aspects of this solution, and concentrate on the modeling itself. Is this indeed a two-player game? Will the threat strategy work? Well, if Israel and the Palestinians were the only sides in the business, then the answer to these questions may have been positive. But this is not the case. There are other players in this game: Hizbollah, Iran, US, and many other Arab and European countries. Leaving them outside the model misses an important aspect of the interaction. For example, Hizbollah and Iran may react to Israel’s threat strategy. That is, they may themselves threat Israel that if it implements its threat strategy, they will implement a threat strategy of their own, so that in fact Israel do not choose between “do nothing” and “react with a missile”, but between “do nothing” and “start a full-fledged war”.
Suppose that one week after Israel sets its automatic machine, Hizbollah sets its own automatic machine: if Israel shoots a missile into Gaza, Hizbollah’s machine shoots ten missiles into Israel. And then Israel will build another machine to threat Hizbollah. And then Iran will build a machine. World War I started because of such automatic machines. If we let countries build automatic machines that react to the other side’s agressiveness, we will end up with World War III that will start because some small Palestinian organization shot a missile into Israel (in the hope of starting a full-fledged war).
I may have missed something in the game theorist suggestion, and the journalist may have missed something in his report. But what the newspaper readers get from the interview is that game theory says that the simple solution of automatic machine will work. I fear that game theory does not say that. And I fear that contrary to what the game theorist perceived, it will not work.