Liberman put Netanyahu and Gantz in the prisoners’ dilemma - analysis

An introduction to game theory from Nobel winner Robert Aumann can help us analyze the political situation.

Avigdor Liberman at the Maariv/Jerusalem Post election conference on September 11 (photo credit: MARC ISRAEL SELLEM)
Avigdor Liberman at the Maariv/Jerusalem Post election conference on September 11
(photo credit: MARC ISRAEL SELLEM)
Yisrael Beytenu leader Avigdor Liberman presented Prime Minister Benjamin Netanyahu and Blue and White chairman Benny Gantz with his plan on Saturday night: Netanyahu must give up on his 55-seat right-wing bloc, and Gantz must accept the “president’s plan” for a rotation for prime minister so that they can form a national unity government. If one doesn’t compromise, Liberman will support the other.
Both Netanyahu and Gantz began a series of consultations with their closest allies, advisers and leading figures in their parties. But one name has yet to be mentioned in the people consulted: Prof. Robert Aumann, the mathematician who won a Nobel Prize in Economics for his work in game theory.
Liberman has put Netanyahu and Gantz into a situation that resembles one of the best-known examples of game theory: the prisoner’s dilemma.
In previously unpublished remarks, Aumann discussed with The Jerusalem Post last year the application of game theory to politics. He explained that “game theory is the science of entities that are striving to different goals and are interacting with each other. It is the science of strategic interaction…You’re doing the best you can, while taking into account that the other players are also doing the best you can,” and vice-versa.
Aumann said last year that he’s not a news consumer, but his wife tells him what he needs to know.
Still, he has some thoughts about how game theory can be used in politics. Game theory is best used in areas that are not zero-sum games: “If you look at political parties as players, then they have much in common,” he said. “They are striving to different, but not opposite goals.
“The most important word in game theory, in non-zero sum situations, is incentives. When you’re in a game with someone else…you have to give them incentives to do what is good for you. Which means if you give them incentives and they do it, it’s good for them too. It should be good for both sides…The bottom concept is that people pursue what they think is to their advantage.”
Now that a Nobel laureate has given us Game Theory 101, we can see where it applies to our current situation.
The prisoner’s dilemma, the best-known game in game theory, posits that two criminals are arrested and put in prison, with each in solitary confinement and unable to communicate with the other. Each prisoner is offered the chance to betray the other and say he committed the crime, or cooperate and stay silent. If A and B betray each other, then they stay in prison for two years each. If A betrays B and B stays silent, A will be released and B will get three years in prison, and vice-versa. If neither rats out the other, both will serve a year in prison.

 

If we were to redraw the prisoner’s dilemma matrix for our political situation, it would look like this: if neither Gantz nor Netanyahu compromises, we’ll have a third election. If Gantz compromises and Netanyahu doesn’t, then Liberman will support Gantz forming a government, and vice-versa. If both compromise, then they can form a unity government.

 
From that chart, it seems that there is a clear advantage to compromise for both sides. Whoever compromises will be prime minister, either alone or in a rotation agreement. And it is the best for this country since, at least publicly, everyone involved thinks a third election is a bad option.
If only things were so simple.
Aumann himself admits that game theory is not everything in politics. When he spoke to the Post last year, he refused to comment on current political events. But the interview took place in December, shortly after Naftali Bennett made an ultimatum to Netanyahu: appoint me defense minister or I’ll quit and your coalition will fall apart. Bennett then backed down from his ultimatum, and said that he sought Aumann’s advice.
The mathematician, who is outspoken about his right-wing views, told Bennett that quitting was the right thing to do according to game theory, but it was not the right thing for the country. In the end, the coalition fell apart a few weeks later, and Bennett became defense minister this week, nearly a year later.
In any case, both Gantz and Netanyahu are having a difficult time making a decision. The right thing to do according to game theory is not the obvious right thing for either of them to do at this juncture.
For Gantz to accept Liberman’s terms, he would likely have to break his campaign promise not to sit in a government led by a prime minister under indictment, and those indictments are expected to arrive in the coming weeks. Likud is demanding that Netanyahu be prime minister for the first year after the government’s formation, or when his trial begins. In addition, the other leaders of Blue and White – Yair Lapid, Moshe Ya’alon and Gabi Ashkenazi – do not trust Netanyahu, and think he would sabotage Gantz and find a way not to hand over the premiership.
For Netanyahu, accepting Liberman’s game plan could mean he ends up with nothing. If Netanyahu agrees to give up on the other right-wing parties in his bloc, then some or all of them could give up on him. Which means that even if Gantz refuses to compromise and Netanyahu agrees, Gantz could still win. Netanyahu does not have that alternative possibility, because if he does not compromise, Liberman has said in that case he won’t join him, and the left-wing parties have promised not to be in any government with Netanyahu.
There’s a dilemma here for Liberman, as well. If one side compromises and the other doesn’t, no matter which side it is, Liberman will have to blatantly contradict himself.
Liberman promised not to sit with the haredim (ultra-Orthodox) unless they make major compromises that are anathema to them, which means that if he supports Netanyahu, the only path to a government means going back on his word.
If Liberman ends up supporting Gantz, the only practical option at the moment is for the Blue and White leader to form a minority government supported by the Joint List. And even that is not super-realistic due to strong opposition in the right-wing branch of Blue and White. But let’s say Gantz pursues it. Liberman has practically built his career on his rhetoric toward Israeli Arabs – one past campaign slogan said “Only Liberman speaks Arabic,” and another said “no citizenship without loyalty,” representing his call for Israeli Arabs to have to make loyalty pledges to the state. In recent weeks he has repeatedly called the Joint List a “fifth column” and supporters of terrorists. And even if Liberman doesn’t join Gantz’s minority government and only facilitates it – by having Yisrael Beytenu MKs be absent for the vote to authorize its formation – he’ll have cooperated with the whole enterprise, which will be a fatal blow to him in his right-wing voter base.
In this scenario, the state attorney offering the prisoners the deal – aka Liberman – also has plenty to lose. For now, all we can do is wait and see who wins the game.