fight each other vs fight with each other

Examples:

• The two rival gangs decided to fight each other for control of the territory.
• The siblings always fight each other over the smallest things.
• The two countries have been fighting each other for decades.
• The teams will fight each other in the championship match.
• The candidates will fight each other in a heated debate.

Alternatives:

• battle each other
• compete against each other
• clash with each other
• wage war against each other
• engage in conflict with each other

Examples:

• The allied forces fought with each other to defeat the enemy.
• The siblings fought with each other to overcome their differences.
• The team members fought with each other to achieve victory.
• The classmates fought with each other to complete the project on time.
• The countries fought with each other to combat the global threat.

Alternatives:

• collaborate in fighting each other
• work together in battling each other
• unite against each other in conflict
• cooperate in combat with each other
• join forces to fight each other