Carrie Aulenbacher remembers the conversation clearly: Her husband told her he wanted to buy an arcade machine he found on eBay. He said he’d been saving up for it as a birthday present to himself. The spouses sat at the kitchen table and discussed where it would go in the den.

Two weeks later, Ms. Aulenbacher came home from work and found two arcade machines in the garage—and her husband beaming with pride.

“What are these?” she demanded.

“I told you I was picking them up today,” he replied.

She asked him why he’d bought two. He said he’d told her he was getting “a package deal.” She reminded him they’d measured the den for just one. He stood his ground.

“I believe I told her there was a chance I was going to get two,” says Joe Aulenbacher, who is 37 and lives in Erie, Pa.

“It still gets me going to think about it a year later,” says Ms. Aulenbacher, 36. “My home is now overrun with two machines I never agreed upon.” The couple compromised by putting one game in the den and the other in Mr. Aulenbacher’s weight room.

It is striking how many arguments in a relationship start with two different versions of an event: “Your tone of voice was rude.” “No it wasn’t.” “You didn’t say you’d be working late.” “Yes I did.” “I told you we were having dinner with my mother tonight.” “No, honey. You didn't.”

How can two people have different memories of the same event? It starts with the way each person perceives the event in the first place—and how they encoded that memory. “You may recall something differently at least in part because you understood it differently at the time,” says Dr. Michael Ross, professor emeritus in the psychology department at the University of Waterloo in Ontario, Canada, who has studied memory for many years.

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