EliNoam Horesh
One Jew, three opinions.

‘Mowing the Lawn,’ Penalty Kicks, and Nash Equilibria

A soccer ball in the foreground, teed up in front of the goal in the back. Credit: Michal Jarmoluk,

Six months on from October 7th, the sleeping giant of the political Israeli public is waking up. Though up until now, real accountability is on the back burner, and most maneuvers to bring down the government are coming primarily from within the the Knesset Plenum, there can be no doubt that patience in the public square is running out. Answers on how Israel got to the point where the Hamas massacre was possible, and even worthwhile for Hamas Gaza Chief Yahya Sinwar to order, are going to be an important component of justice. Using a classic example from Game Theory, we can evaluate one of the longest-term strategies employed by Israeli political and military leaders in the lead-up to October 7th, and understand its long-term effects on incentive structures in the Conflict.

The Penalty Kick Game is one of the most riveting parts of any football match, turning up the heat up by distilling the entire match into a sudden-death, mano-a-mano psychodrama. Additionally, it is one of the most recognizable examples of the Mixed-Strategy Nash Equilibrium, a concept taken from Game Theory. This field is the study of competitive behavior between individuals and groups through psychological and statistical analyses and is regularly used in such disparate topics as psychology, economics, and computer science.

In many ways, Israel and Hamas have been playing a version of the Penalty Kick Game for the last two decades. In the years leading up to 2005, Prime Minister and famed general Ariel Sharon championed the Disengagement Plan, a radical new direction that sought an end to diplomatic peace initiatives with the Palestinians, in favor of a unilateral posture. The pitch was thus; let’s wash our hands of the land we conquered in 1967, and should the Palestinians ever try anything, Israel can capably handle them. Following Operation Defensive Shield in 2002, having squashed Palestinian Militias in all major cities in the West Bank, Sharon’s vision of “hot” peace seemed attainable and attractive.

In The Penalty Kick Game, there are two players; the kicker and the goalie. The kicker can choose to either kick on his dominant side, or he can kick to his non-dominant side, anywhere within the goalposts. So too, the goalie must block either by jumping to his right, or his left. After 5 kicks to either goal, the team that made more goals wins. In the rules of this game, outcomes are zero-sum. When one scores, they gain a relative advantage, +1, and the other loses -1. 

Critical to understanding this model is the concept of the Nash Equilibrium. The Nobel Prize-winning theory of strategy states that, in any non-cooperative two-player games, there is at least one strategy per player that is impossible to improve upon, because it neither offers better maximization of benefit nor does it offer better minimization of risk. In the Penalty Kick Game, neither kicking nor jumping left or right maximizes the chances of benefit. The entire area between the goalposts is, essentially, a mixed-strategy zone, where any place is as good as any other to kick at. The case of the Penalty Kick Game then, so straightforward, is the textbook example of Mixed-Strategy Nash Equilibria. Victory and defeat are as random as the placement of a well-aimed football.

Ariel Sharon, the Israeli strongman, never saw out his vision for total disengagement from the Palestinians, but the reality of the Gaza Strip post-2005 is, in realist terms, more-or-less the best case for Israeli security. Unilateralism became the de-facto policy of the Israeli Right, who believed that Palestinians could and should self-administrate, so long as they didn’t infringe on the safety or consciences of the Israeli public. Following the Two Intifadas, the proactive Israeli left was in ruins, and most Israelis had little faith in Palestinian goodwill. As political analyst and lobbyist David M. Weinberg prescribed in response to 2018’s incendiary balloon attacks, Israel would periodically “mow the grass,” avoiding major conflict while responding to intermittent threats as they arise.

Weinberg of course frames Israel as the proactive player, doing the “mowing.” A better view of this unilateral policy is that Israel assumes the role of the goalie, and Hamas assumes the proactive role of the kicker. This is heuristically true, if you take as fact Benjamin Netanyahu’s claim that “If the Arabs put down their weapons today, there would be no more ‎violence. If the Jews put ‎down their weapons ‎today, there would be no ‎more Israel.‎”

In this analogy, Hamas’ available “kicks” are all equal in their ineffectiveness; tunnels, rockets, incendiary balloons, threatening propaganda, or blubbering to useful idiots in the West, are strategically all relatively similar in terms of the maximization and minimization. Israel must always defend itself, through import embargos, targeted assassinations, public communication campaigns, Iron Dome, airstrikes on military installations, and occasionally the odd ground–invasion. As the political class of October 6th would tell it, this was a dance that Israel was destined to play forever, or at least until Palestinians straightened themselves out. The onus to provide a real solution for the conflict did not lay at Israel’s feet.

Prime Minister Netanyahu, as the inheritor of Sharon’s unilateral posture vis-a-vis the Palestinians, overlooked one critical aspect of the long-term game at hand. Critically, the classic Penalty Kick Game is zero-sum. In a true football match, with two teams taking shots at one another’s goal, there are only ten turns to play. In a situation like this where there are no more than ten kicks total each goal that the kicker misses is, in effect, +1 for the goalie and –1 for the kicker. The goalie functionally gets a point when the kicker misses. This assumption of zero-sum holds only if the game is finite, and if both teams take turns being the proactive agent. 

The conflict is enduring. In 19 years since the disengagement, Israel has “mowed the lawn” no fewer than 17 times. That is to say, Israel has responded to provocation or threat from Hamas in the Gaza Strip no fewer than 17 times. Without the constraints of a structural end to the game, Hamas “missing a shot” can’t be considered –1, and Israel preventing major destruction can’t be considered +1. The only way Hamas loses is by being forced out of the game, and the only way they win is if they score a goal and, crucially, they only need to score once. 

This dynamic plays nicely into Hamas’ ideology that survival is victory, as well as more generally the immoral arc of history that Islamists around the globe believe in. While Israel has to consistently defend their goalposts every single time, Hamas only has to score once. By giving up on the Palestinians as partners for peace, and by believing, with great hubris, in our own military infallibility, Israelis entered into a version of The Penalty Kick game that was, in effect a ticking time bomb. All that Hamas needed to do was wait for us to take our eye off the ball.

About the Author
EliNoam is an Israeli-American student of Economics and Political Science at Hebrew University and Jerusalem Volunteer Coordinator for the "Big Brother For Lone Soldiers" program. He is a former field intelligence specialist in the IDF, and a Sergeant Major in active reserves. Opinions and analyses are exclusively EliNoam's, and do not reflect the positions or policies of his employers.
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