What Game Theory Tells Us About the Threat of an Israel-Iran War

Each side must predict how the other will react to avoid mutual destruction.

For years, the conflict between Israel and Iran had unofficial but fairly clear rules, allowing the enemies to maintain an uneasy equilibrium in the Middle East.

Neither wanted all-out war, so both kept within certain boundaries. At times of rising tension, they stepped back from the brink.

Scholars of game theory say this is a common pattern. In conflicts that simmer over many decades, tit-for-tat actions and reactions often develop into mutually understood “rules of the game” that deter open warfare, said Daniel Sobelman, a professor at Hebrew University in Jerusalem. He is literally writing the book (or at least a book) on game theory in the region, as author of the forthcoming “Axis of Resistance: Asymmetric Deterrence and Rules of the Game in Contemporary Middle East Conflicts.”

But the events of the past few weeks, including Israel’s successful attacks on Iran’s proxy in Lebanon, Hezbollah, and the volley of ballistic missiles that Iran launched against Israel on Tuesday night, have demonstrated that the old rules no longer apply.

Now, the question is whether Israel and Iran will reach a new equilibrium that stops short of a full-blown conflict — or if the dangerous new mix of uncertainty and aggression will send the Middle East spiraling into all-out war.

War games

It is an idea that sounds so simple as to be almost callous, yet its implications are so powerful that it won a Nobel Prize: Wars — both fighting them and preventing them — are essentially games of prediction.

That’s an important cornerstone of game theory, a method of analyzing the strategies that different “players” — be they militaries, business rivals or poker players — choose to achieve the best possible outcome for themselves.

When it comes to war, each side needs to forecast how the other will react to a given move in order to weigh its costs and benefits. And by credibly demonstrating that the costs of aggression would be too high to be worthwhile, even bitterly opposed enemies can deter a catastrophic war.

That theory will be familiar to anyone who has watched Hollywood movies like “War Games” or “Fail Safe,” whose plots turn on understanding that the best way to avoid a catastrophic nuclear war is to convince your opponent that any attack would lead to its annihilation.

But it doesn’t only apply to nuclear war. Other forms of conflict, including long-running tensions like those between Israel, Iran, and Iran’s proxy militias, also center on one question: What action should I take to advance my interests and keep my opponent from imposing greater costs than I am willing to bear?

Israel was always stronger militarily than Iran, particularly when its close alliance with the United States was factored into the equation. But Iran cultivated the militias known as the “axis of resistance” — including Hezbollah in Lebanon, Hamas in the Gaza Strip and the Houthi rebels in Yemen — that posed a credible threat that the costs of full-blown war would be too great for Israel to bear.

“Hezbollah in particular was a big part of that threat,” said Emma Ashford, a senior fellow at the Stimson Center, a nonpartisan research institute that studies peace and security. “It was, ‘If you do something against Iranian interests elsewhere in the region, Hezbollah will launch a massive rocket attack from Lebanon. And you know, you don’t want to cross that line.’”

Oct. 7 changes the balance

That equilibrium was damaged but not broken on Oct. 7, 2023, when Hamas fighters attacked Israel, massacring civilians and taking some 250 hostages. Hamas clearly wanted its attack to be the opening salvo in a regional conflict between Israel and the entire Iranian axis, but Hezbollah and Iran quickly communicated that they did not want to escalate.

Hezbollah began firing rockets at Israeli positions on Oct. 8, but in a way that suggested that it expected Israel to keep its response restrained and symmetrical, Sobelman said.

Israel, for its part, “didn’t want to fight a two-front war, and therefore it was doing enough to dissuade Hezbollah from pushing its luck,” said Lawrence Freedman, an emeritus professor of war studies at King’s College London. For most of the last year, that was enough to maintain a stable if hostile dynamic between Israel and Hezbollah. They regularly exchanged attacks, but kept them relatively mild in comparison to the heavy fighting in Gaza.

For a time, that deterrence strategy seemed to hold: actions were met with proportional responses, avoiding an all-out war.

In April, there was a moment of uncertainty that brought new risks of miscalculation. Israel bombed an Iranian diplomatic compound in Syria, killing three top Iranian commanders and four other officers. In retaliation, two weeks later, Iran launched a barrage of hundreds of drones and missiles at Israel. The week after that, Israel struck an antiaircraft system that protects a nuclear facility near the city of Isfahan.

Those strikes, while an escalation of the conflict between Israel and Iran, nevertheless fit within the longstanding framework for deterrence between the two countries. Because the diplomatic compound was in some ways an extension of Iranian territory, “it made sense in the context of symmetrical rules of the game that they would retaliate directly against Israeli territory,” Sobelman said.

And while Iran’s strike on Israel was unexpectedly large-scale, the weapons it used meant that Israel and its allies were able to intercept the attack, preventing significant damage. Israel’s limited strike in retaliation was a signal that the escalatory exchange had ended — that it would “take the win,” as President Biden reportedly urged Israeli Prime Minister Benjamin Netanyahu to do.

When the old rules no longer apply

But now that equilibrium has faltered. Israel sharply escalated its actions against Hezbollah in mid-September when it detonated hundreds of explosives concealed in pagers and two-way radios that it had covertly distributed to the armed group, dealing a serious blow to its leadership. Days later, it began a heavy bombing campaign in Lebanon. And on Sept. 27, it killed Hassan Nasrallah, the leader of Hezbollah and one of the most powerful figures in the Iranian axis.

Game theory suggests that ultimately, the weaker party — Iran and its proxies in this case — is the one responsible for preserving deterrence, Sobelman said. “The onus is on the weaker actor to restrain the stronger side,” he said, by acting in a way that shows that an all-out conflict would lead to intolerable harm.

So under the unwritten rules of the game, Israel’s recent attacks on Hezbollah should have provoked a devastating response from the armed group, Sobelman said. “Theoretically, there should’ve been thousands of Israeli fatalities,” he said. “There should have been high-rise buildings going down in Israel.” But that didn’t happen. Whether because Israel’s attacks have been so devastating that Hezbollah no longer has the ability to retaliate, or for some other reason, the expected response never came. The deterrent Iran had relied on to keep the conflict at a manageable level appeared, for practical purposes, to have collapsed.

“Deterrence has failed,” Ashford said. “The Iranians now have to figure out, can they stop Israel or the U.S. from crossing more of their red lines?”

The danger of uncertainty

Iran’s attempt to answer that question seems to have come on Tuesday night, when it fired more than 180 ballistic missiles at Israeli soil, a significant escalation in direct hostilities. Because Iran’s targets included the urban area around Tel Aviv,, the attack was widely seen as crossing a new threshold even compared to the April attack, which only targeted military bases and relied partly on weapons that were easier to intercept.

But that doesn’t necessarily mean that Iran is trying to escalate the conflict. In fact, that kind of escalation can be used to deter an open conflict, rather than start one, Sobelman said.

However, the danger is that without the clarity of the rules that governed the conflict for so long, either side could misjudge and overstep, taking action that provokes a much stronger retaliation than they anticipate. “You’re not restoring what existed before,” Ashford said. “You’re moving to some new equilibrium. And that equilibrium could be similar, better, or it could be worse, if either side misinterprets.”

“It’s a very, very dangerous thing,” she said.

Sobelman, who has studied Iran and its proxies for decades, said that he believes that Iran was trying to deter Israel, not to begin a new era of direct conflict between the countries. In the missile attacks on Tuesday night, Iran was “trying to establish a certain deterrence threshold that would bring this escalatory cycle to closure,” he said. “It was trying to retaliate in a certain fashion that would deter Israel from further escalation.”

The question now is whether Israel will see it that way — and, even if it does, whether the Israeli government will view this moment as an opportunity to do further damage to Iran now that the threat of retaliation by Hezbollah seems to have been substantially reduced.

If that happens, it is not clear how far the situation might escalate, or how the United States and other Israeli allies would react if it did.

One likelihood is that the heaviest burden of any miscalculation or renegotiation of the rules would fall on civilians.

Israeli attacks in Lebanon have displaced approximately a million people from their homes in recent weeks, according to the United Nations, and killed at least 1,600, according to Lebanese health officials, though the death toll does not distinguish between civilians and combatants.

Approximately 60,000 residents of northern Israel have been displaced for the past year because of the threat of Hezbollah rocket attacks. And the sole confirmed death from Iran’s missile attack Tuesday night was Sameh al-Asali, a laborer from Gaza who was sheltering in the Israeli-occupied West Bank — one more victim of the dangerous uncertainty about the new rules of the game.

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