Nash equilibrium is the point where each player is making the best move available given what the other player is doing. Nobody loves the outcome, but nobody can improve their position just by changing alone. In geopolitics, that often looks like stalemate, arms races, tense deterrence, or a frozen confrontation that both sides keep hating but keep reproducing.
The prisoner's dilemma explains why rivals often defect even when cooperation would leave both better off. If each side fears being the sucker, both choose the safer hardline option. That is why disarmament is difficult, why tariffs spiral, and why military buildups often continue even when they are irrational in aggregate.
The chicken game is different. Here the danger is not silent mutual defection but public escalation. Each side tries to look more resolved than the other, hoping the opponent swerves first. Taiwan, naval brinkmanship, and trade escalation often fit this structure better than classic prisoner's dilemma models.