Comity

Comity refers to courts of one state or jurisdiction respecting the laws and judicial decisions of other jurisdictions – whether state, federal or international – not as a matter of obligation but out of deference and mutual respect. 

In Constitutional Law, the enforcement of judgments between states in the United States is governed by the Comity Clause of the Constitution - Article IV, § 2, Clause 2.

The first-filed rule, for instance, is a rule of comity for resolving conflicts of jurisdictions where parallel actions are filed in different federal district courts. If two or more substantially identical actions are proceeding in different courts, the court with the action that was filed later should defer to the jurisdiction of the court with the action that was filed first by dismissing, staying, or transferring the later-filed suit.

See also: comity of nations