Irony is an important literary element in both of Ambrose Bierce's stories. In fact, it is pretty central to most of his writing. In "Occurrence," the irony is two-fold. One aspect is that Peyton thinks that destroying the bridge will help the situation, when ultimately, that is where he meets his death. In addition, it is ironic that just as the noose tightens around his neck, he thinks he escapes, when in reality, he dies.
In "Chickamauga," the irony is that while the young boy plays soldier, there are grown soldiers in real life all around him. Bierce makes a statement that war adversely affects everyone and when we show children how to wield swords and fight, they will one day take part in real wars and die. In both stories, Bierce effectively uses irony to convey a sense of the tragedy and consequences of war.