Time for some game theory about the recent development in Israeli politics. (You can read more about it here)

In the aftermath of the last election, no side could form a governing coalition. So the options were either a unity government, composed of the two major parties (Bibi Netanyahu’s Likud and Benny Gantz’ Kahol-Lavan) or yet another, fourth in a row, election. But with a year of election campaigns sowing hatred throughout the country, the ongoing coronavirus lockdown and an impending recession, nobody wants another election. So the two factions have to bargain on the terms of the unity government, with the possibility of another election being what game theorists call a disagreement point: this is what happens if negotiations break down.

Game theory teaches us that the disagreement point has a significant impact on the outcome, even when the parties reach an agreement, and that the better your position in the disagreement point, the better the bargaining outcome will be for you.

The disagreement point in the negotiation following the last election is impacted by two factors that did not exist in the previous rounds:

  • The coronavirus came as a gift from the gods for Bibi. Frightened citizens usually stick with incumbent leaders in times of crisis, and in Bibi’s case, this tendency is magnified by the fact that he has been around for so many years. Even before the virus popped up, the greatest difficulty of the opposition was to convince the public that he is not the only person who is qualified for the prime-minister job. So an election will be advantageous to Bibi. Moreover, since the election will be postponed until after the lockdown, Bibi will likely stay in power for a long period even under the disagreement point.
  • While he could not form a government, this time Gantz did manage to form a functioning majority coalition in the parliament. He was on the verge of electing a parliamentary speaker from his party, which would allow him to implement a law — the so-called “Bibi law” that forbids Bibi from being appointed for a  prime-minister due to the fact that he was indicted for bribery.

So, in terms of the disagreement point, Bibi has something good going for him and something bad going for him. So he made a threat: If you continue with your current plan to take over the parliament, I will abandon the negotiations and we will jump straight ahead to the disagreement point. Gantz, believing the threat, gave up on the plan. Instead, he promised to give the speakership to somebody from Bibi’s party and to join a government led by Bibi and, and he has split his own party for that purpose, bringing with him only half of it to the new coalition under Bibi.

So now Gantz made the disagreement point much better for Bibi and much worse from himself:
— If there is an election again, Gantz will be viewed as a fool who tore down his party for nothing, and he will likely not be elected.
— Gantz has made public that he too thinks Bibi should be a prime minister. This statement substantiates Bibi’s image as the only qualified person for the job. It also diminishes the moral argument against choosing an indicted person to prime-minister, which was the justification for Bibi’s law and a central theme in the campaign against him.
— Gantz currently took the speakership to himself. Joining Bibi’s government will force him to resign from the speakership, and he has already agreed to give it to Bibi’s party. After Bibi has the speakership, even before the government is formed, it is not possible to pass the Bibi law.

The alternative was to take over the parliament, uncover information about the government’s lack of preparation and incompetent handling of the corona crisis, and meanwhile negotiate secretly over the unity government. But without publicly supporting Bibi as the prime-minster until the deal is reached, all the while keeping the option of passing Bibi’s law if the negotiation fails. It’s hard to predict a bargaining outcome, but I think it is possible that under this plan, even if Bibi would have continued to be the prime minister for some time, we would see a meaningful division of power and a date for the termination of Bibi’s reign. Now there is no such hope.

Why did Gantz give up all his cards? I think the reason is that, because he believed in Bibi’s threat to abandon the negotiations, Gantz thought he had to choose between another election and a unity government. Indeed, Gantz conducted an election poll before he made this move, which suggests he was thinking in these terms.

Bibi’s threat, however, was empty, or, to use another game-theoretic jargon, not credible. The fact that the disagreement point would have become worse for Bibi precisely implies that, whatever he says now, he would have been willing to negotiate in order to escape it. The only difference is that the negotiation would be conducted in an environment that is less convenient to Bibi.
It is also not at all clear that the probability of reaching a deal has increased following Ganz’s move. In fact, an exultant Bibi might insist on terms that even Gantz will not be able to accept.

Many of Gantz’ voters are furious because they preferred another election over a Bibi government. But Gant’s voters who were willing to stomach a Bibi government should also be furious because Gantz created a bargaining environment in which he is desperate to achieve it.