(battle|clash) of wills

a situation involving two people who refuse to compromise, hoping the other individual does so first

The idiom "battle of wills" originated from the concept of individuals or entities engaging in a struggle or conflict based on their strong and opposing desires, intentions, or determination. This expression is mainly used to convey the idea of a confrontation or disagreement where each side is unwavering and resolute in pursuing their own objectives, often resulting in a protracted and intense struggle.

The negotiation turned into a battle of wills as both parties refused to compromise on their key demands, resulting in a deadlock.
The parent and the child engaged in a clash of wills over bedtime routines, with each stubbornly asserting their preferences and refusing to back down.
The legal dispute became a clash of wills between the opposing attorneys, with both determined to win their case at any cost.
The project team experienced a clash of wills when members had conflicting ideas about the project's direction, leading to heated debates and delays.
The political leaders engaged in a battle of wills during the negotiations, each trying to assert their influence and control over the decision-making process.