“Mission Accomplished.” This phrase has haunted US foreign policy ever since George W. Bush stood on the deck of USS Abraham Lincoln in 2003 and declared victory in a war that would drag on for another eight years. It has become shorthand for a particular kind of strategic self-deception: the gap between what a military operation achieves and what its architects claim it has achieved.

As the confrontation around the Strait of Hormuz grinds into its second month, such a gap is opening again. Game theory, the mathematical study of strategic decision-making, can help explain why.

In a conventional military confrontation, few can match the combined might of the US and Israel. Their high-tech arsenals with precision strike capabilities have inflicted real and substantial blows on Iran. By any traditional scorecard, this alliance is winning.

But this is not a conventional confrontation. It is a war of attrition – a situation where two or more “players” are engaged in a costly showdown where each player remains active in the hope that the opponent will eventually yield. In this situation, game theory says that victory doesn’t go to the stronger party, but to the one able to endure the losses for longest. That distinction changes everything, because time is the one resource that favours Iran.

Iran’s costs, though significant, seem to be tenable. Its regime has shown a remarkable capacity for regeneration: remove one layer of command and another takes over. Its stockpile of missiles and cheap, mass-producible drones keeps replenishing faster than it is depleted.

For the US, it’s a different story. Maintaining naval dominance in the strait demands continuous, expensive deployment. Every intercepted drone, every carrier group rotation, every diplomatic effort to hold a fracturing coalition together adds to a bill that compounds over time. In a war of attrition, that growing asymmetry of costs matters more than the balance of firepower, and it is not running in the US’s favour.

Blurred objectives

This structural reality may explain something that has puzzled many people: why the Trump administration has never clearly defined what winning looks like. The ambiguity is not accidental. When battlefield arithmetic is unfavourable, game theory says that blurred objectives become a strategic necessity.

Before you can identify rational strategies and predict the outcomes of a game, you must first identify what each player is trying to achieve. Yet the goalposts keep shifting.

The conflict did not begin over the strait. Its original objectives were about regime change, degrading Iranian nuclear infrastructure, and breaking the Islamic Revolutionary Guard. That those goals have receded, overshadowed by the narrower imperative of controlling the strait, suggests the campaign has lost momentum.

Game theory, however, points to a double edge in this strategy: ambiguity cuts both ways. A player who never commits to clear objectives retains the freedom to declare victory and exit.

Blurred objectives preserve flexibility in a way that explicit commitments never could: a player with undefined goals cannot be held accountable for failing to reach them and, if skillful, can even be credited for reaching them. President Donald Trump has used this approach often throughout his two presidencies.

There is a further constraint: time. Research on the political economy of conflict suggests that leaders facing electoral deadlines are under particular pressure to end wars of attrition well before voters pass judgment. With midterm elections approaching, Trump’s window for a credible exit is narrowing fast.