Chicken is a very common game theory problem which has a ridiculous name. Often, academics will refer to it as "mutually assured destruction," but both names demonstrate the problem pretty well.
In "Rebel Without a Cause," James Dean and his rival get wrapped up in a game of chicken. Each drives their car towards the edge of a cliff. The first one to leap out of their car is a coward, and the other has proved their superiority. Since neither player wants to be a coward, they continue driving towards the cliff. This is a stupid game.
There are two states of this game where both players are equals: both keep driving, and both stop driving. One of those states means both players live. However, as long as the game starts with driving, both players will continue as long as they are unwilling to become the coward and allow the other player to win.
Chicken describes a clash when neither player are willing to back down. It describes arms races like Global Nuclear Proliferation and the Cuban Missile Crisis but also the one between min-maxing players and the resulting disgruntled authors in Pathfinder Organized Play.