In the wake of agreeing to a two-week cease-fire on April 7, both the United States and Iran are claiming victory in their war. Each says the same thing: We held out and the other guy blinked first. In fact, both decided to call it a draw. And some sort of outcome like this was always likely, because the structure of the game constrained the decision-making of the players—even players as idiosyncratic as U.S. President Donald Trump and the leaders of the Islamic Republic.

Wars have three phases: an opening, a middle game, and an endgame. As in chess, the opening involves deploying forces and engaging the enemy. If that doesn’t produce a quick victory, the contest moves into a middle game in which the two sides fight it out and try to get one another to surrender. As the trends in battle become clear, eventually the rough shape of a logical outcome emerges and the war enters its endgame, during which the details of the final settlement are hammered out.

In Iran, the endgame began with Trump’s threat of massive destruction if Iran did not open the Strait of Hormuz, and it will continue until the belligerents come to a stable agreement ending hostilities. The cease-fire is likely to hold for the same reason it was agreed to in the first place: both sides were hurting and would hurt even more if the war escalated instead of ending.

The Trump administration launched the war confident that the conflict would be relatively quick and cheap and that Iran wouldn’t be able or willing to hit back. Neither assumption proved true, and as the fighting continued, the war started looking not like chess but a deadly game called “the dollar auction,” which traps the players in unprofitable escalation.

The concept is straightforward: Two players bid for a prize of one dollar, with both agreeing to pay their last bid whatever happens. At first, the players bid eagerly in hopes of making a profit. As the price rises, the trap springs shut. The first player to bid $1 would come away even. But the other player would be out almost a dollar (his last bid)........

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