Although many people are using principles of game theory to analyze the Trump/Iran war and to predict the next steps, I haven’t come across an explicit model. Any model drastically oversimplifies reality but also serves to clarify assumptions.
The model that I present is essentially a Prisoner’s Dilemma. For each side, it is better to continue deadly offensive operations than to cease, regardless of what the other side does. Therefore, the model predicts that the war will continue (bottom-right box) even though both sides would be somewhat better off with a mutual ceasefire (top-left). That’s how a Prisoner’s Dilemma works.
The model presumes that both sides have the capacity to continue offensive operations–that the US won’t run critically low on munitions and Iran will retain drones, missiles, mines, and possibly sleeper cells abroad. To the extent that the US and Israel have a plan, it is to destroy Iran’s military assets so that Iran cannot choose to continue to bomb or lay mines. I cannot assess whether this is possible, but it seems doubtful. The recent reduction in the tempo of Iranian strikes may simply reflect a strategy of operating for a longer period.
The model is symmetrical, which is misleading. The Iranian leader, Mojtaba Khamenei, has already lost his father, wife, daughter, son-in-law, and 14-month-old granddaughter in a strike and could be killed himself. More than 1,000 Iranians (and probably many more) have died so far. Donald Trump is much safer, as are American citizens–presumably. On the other hand, Trump’s political fortunes are sensitive to exactly what happens in the war, whereas Khamenei and his team are trying to survive. For them, a difference in the length of the conflict or the number of casualties may be immaterial.
Another way that the model simplifies is by reducing the whole war to two parties. Israel is not shown. Nor are other major countries, such as Russia, China, Saudi Arabia, and others. Also, the two sides are shown as if they were unitary, but there are internal conflicts on both sides. In fact, each leader may care most about the struggle with his own domestic opponents. However, to some extent, that dynamic is captured by the outcomes shown in the model. For example, each side benefits domestically from being able to claim victory credibly, and each side loses domestically if it cannot.
See also: making our models explicit; Brag, Cave and Crow: a contribution to game theory


