The 12-day war between Israel and Iran may have paused—but the next round of violence is already taking shape. As of writing this piece, the 12-day war has been halted by a fragile ceasefire—one that could collapse at any moment. While the possibility of renewed hostilities is high, the more pressing question is whether the 12-day war was predictable and whether the continuation of the conflict can be anticipated based on underlying realities.

This is where game theory can help us assess how likely the emergence of a new round of hostilities may be. International relations is often seen as a domain of uncertainty and vagueness, but in this cloudy landscape, game theory can provide a faint light of determinacy. And that determinacy matters. Understanding escalation probabilities is not an academic exercise; it is essential for policymakers and regional actors deciding whether to intervene, mediate, or prepare for the next round of conflict. But first, some context.

An Old Conflict, Deep Ideological Roots

The military tension and hostile interaction between the Islamic Republic and Israel is not a new phenomenon. It began the moment the 1979 Iranian Revolution upended the Middle East. From its inception, the Islamic Republic’s revolutionary identity was steeped in anti-Israel sentiment. Khomeini repeatedly called Israel a “cancerous tumor” that had to be removed, and his successor, Khamenei, elevated the rhetoric further, predicting that ‘there will be nothing called Israel in 25 years.’

This ideological hostility was not merely rhetorical. It has been consistently operationalized through three official policies:

1. Building a regional network of armed proxies (Hezbollah, Hamas, Iraqi Shiite militias, the Houthis),
2. Developing a clandestine nuclear program,
3. Expanding a sophisticated ballistic missile arsenal.

For Israel—a small country with bitter historical experience, a deep memory of the Holocaust, and a low tolerance for existential threats—these ideological declarations, coupled with military capability, are not something to dismiss as hollow gestures.

Game Theory and the Logic of Escalation

Game theory, though not designed for international relations, examines situations where actors interact under conditions of incomplete information, mutual distrust, and strategic interdependence. This makes it uniquely suited for the strategic ambiguity of international relations.

A central concept, Nash Equilibrium, refers to a point where neither actor perceives a benefit in changing its behavior. But this “equilibrium” is not a point of stability. Rather, it may also signify a feedback loop. Two hostile actors can continue contributing to incremental escalation, waiting for the other to blink, until a miscalculation triggers conflict.

This dynamic is not hypothetical. During the Cold War, Nobel laureate Thomas Schelling applied game theory to explain how the United States and the Soviet Union avoided nuclear war despite constant crises. Schelling’s concept of brinkmanship—pushing the opponent to the edge of catastrophe to gain concessions—was essentially a controlled Nash Equilibrium: neither superpower struck first because retaliation would be annihilating, but neither backed down because that would signal weakness. The Cuban Missile Crisis of 1962 became the textbook example of how incomplete information and miscalculated risk can bring the world to the edge.

A similar logic animated Cold War arms races. Robert Powell’s “commitment problem” model explains why states continue to arm themselves, even when both sides recognize the risks: they cannot credibly commit to terminate hostility. The same dynamic is visible in the classic ‘security-dilemma’ which has punctuated some of the more conventional wars. In 1967, Israel’s preemptive strike in the Six-Day War was driven by the belief that Arab states’ rhetoric and troop movements were precursors to attack. Israel calculated that waiting would only worsen its position. Unable to secure a credible peace signal from its adversaries, it opted to strike first—a decision game theory would identify as rational within an equilibrium of mistrust.

The Israel–Iran conflict today is unfolding within this same logic. The absence of direct communication channels, escalating threats, and a long history of deterrence failures create exactly the kind of conditions that game theory predicts will spiral into repeated conflict.

Israel’s Security Doctrine: Jabotinsky’s Shadow

When Polish Jews were being sent to concentration camps, Zionist leader Ze’ev Jabotinsky sent desperate letters to Jewish communities and political actors, warning them not to dismiss the threats of annihilation he had long predicted. His warnings went largely unheeded, but his mode of thinking left a permanent mark on Israeli security doctrine: existential threats must be taken literally.

This doctrine has shaped Israel’s behavior for decades. It was the logic behind the 1981 preemptive strike on Iraq’s Osirak nuclear reactor and the 2007 destruction of Syria’s al-Kibar reactor. Today, Israel views the Islamic Republic as the most serious existential threat it faces—not its Arab neighbors—and Jabotinsky’s calculation still holds: if an adversary threatens annihilation, you must take their words at face value, even if this leads to perpetual conflict.

The October 7 attacks were a Jabotinskian failure—a catastrophic breakdown of deterrence and risk assessment. Since then, Israel has abandoned any pretense of “managing” the threat. Its campaign has since changed course to decapitate Iran’s proxies, sabotage its missile and nuclear infrastructure, and, increasingly, target the regime directly. October 7th also shifted the balance between long-term risk calculation and immediate action for Israel. The attacks strengthened Israel’s resolve to neutralize the threat posed by the Islamic Republic, prompting an unprecedented campaign of assassinations and overt and covert operations, despite the high risk of escalation. This aligns with Bayesian models, in which the incorporation of new evidence increases the actor’s confidence in action. In this context, the new information recalibrated Israel’s probability equations toward more decisive responses, even when they carried higher escalation risks.

For years, the Islamic Republic had cultivated an “agent model” designed to sustain its dominance while carefully avoiding significant escalation. This strategy enabled Tehran to advance its nuclear program while largely evading severe consequences. Post–October 7th, however, this equilibrium collapsed. Israel has demonstrated no hesitation in confronting the escalation dilemma. From targeted killings of Haniyeh and Nasrallah to Operation Rising Lion, each step was taken with full awareness of the potential for escalation. Yet Israel pursued these measures because each increment reduced, however marginally, the existential threat it faced.

Although such decisions may appear to deviate from classical rational-utility models, they can be understood as part of a recalibrated utility function: the perceived gains from eliminating threats outweighed the security risks of escalation. Israel’s military efficiency has underpinned this strategy, even if it has come with reputational and operational costs. The result is an emergent dynamic in which Israel’s decisiveness is reinforced by tangible payoffs, reducing the likelihood that it will pause or reverse the escalation trajectory.

Iran’s Actions vs. Rhetoric

If Israel’s strategic recalibration is best explained by Bayesian logic, Iran’s long-standing strategy has been structured more around the dynamics of the chicken game and the principal–agent dilemma. In game theory, a chicken game describes a situation in which two players move toward confrontation, and each side’s rational strategy is to hold firm in the hope the other will back down first—yet escalation risks catastrophic costs for both. For years, Iran locked its nuclear program in a chicken game dynamic: it could advance its nuclear capabilities without facing an immediate and severe risk of direct confrontation. This balancing act relied on simultaneously keeping a diplomatic channel open for its nuclear program while also leaning on proxy actors across the region.

Proxies in this sense did not merely project Iran’s strategic vision of regional dominance; they also created a deterrent shield around its nuclear program. By threatening retaliatory escalation through Hezbollah, Hamas, or other groups, Iran raised the cost for adversaries—especially Israel—of directly striking its nuclear facilities. At the same time, proxies endowed Iran with a valuable layer of plausible deniability. If an attack occurred, Tehran could deflect responsibility by pointing to autonomous proxy decisions, thereby complicating its adversaries’ response options. This fits the principal–agent model, where Iran (the principal) delegates action to proxies (the agents). While this model extended Iran’s influence, it also created risks of misalignment: the agents could act beyond Tehran’s preferred boundaries, exposing Iran to retaliation it did not directly authorize.

This dual strategy proved effective for a time. Yet, like any game-theoretical strategy, it carried built-in payoffs and potential miscalculations. First, the very reliance on proxies increased Iran’s vulnerability. Once the post–October 7th environment shifted Israel’s calculus, deniability lost much of its protective function. Israel began treating proxy aggression as directly attributable to Iran, collapsing the buffer. Second, the ideological drivers fueling Iran’s strategy—the revolutionary doctrine of resistance and confrontation—elevated the stakes of the game. The higher the stakes, the harder it became to de-escalate, pushing the dynamic toward a tipping point where direct confrontation was no longer avoidable.

Iranian officials, like Abbas Aragchi in a recent interview, claim that “wiping out Israel has never been Iran’s policy.” Yet realities on the ground suggest otherwise. Explicit threats from Khamenei, coupled with material actions—funding proxies, advancing nuclear enrichment, conducting missile tests—make these assurances ring hollow.

October 7 reinforced to Israel that deterrence had failed, and this failure has set the tone for its ongoing offensive posture. But the Islamic Republic, though weakened, is far from neutralized. Its July 21 satellite launch vehicle test, widely interpreted as a cover for ballistic missile development, shows that Tehran is both rebuilding and signaling defiance.

A Dangerous Equilibrium

On the side of the Islamic Republic, the strategic game has shifted from threatening Israel to preserving regime survival. But that change makes Tehran more dangerous, not less. A cornered regime may be more willing to gamble with high-risk strategies, whether through more efficient ballistic missiles or even a preemptive surprise strike. This shift is illuminated by prospect theory, which —a behavioral corrective to classical game-theoretic models—  suggests that actors facing high potential losses are more prone to gamble with greater risks. For Tehran, this means that survival is valued above all else, pushing it toward escalation even when success is uncertain. This dynamic may also explain why, in Operation Rising Lion, Israel hesitated to drive the Islamic Republic into an ‘all-in’ scenario. A pause or measured restraint could have been deliberate, intended to avoid triggering the regime’s loss-driven risk-seeking calculus. Meanwhile, Israel will not scale back its decapitation campaign until it is convinced the existential threat is gone. This is the essence of a Nash Equilibrium: each side continues its pre-existing behavior, not because of guaranteed success, but because deviation is perceived as even riskier. In such a system, deterrence offers no safety; it merely sustains an endless cycle where risk itself becomes the only constant.