die Austragung
staging
The carrying out or organization of an event, especially a sports competition.
Die Austragung der nächsten Weltmeisterschaft findet in Katar statt.
The staging of the next World Cup will take place in Qatar.

staging / resolution
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staging
The carrying out or organization of an event, especially a sports competition.
Die Austragung der nächsten Weltmeisterschaft findet in Katar statt.
The staging of the next World Cup will take place in Qatar.

'Die Austragung' (staging/resolution) is a noun derived from the verb 'austragen'. The ending '-ung' turns the action of the verb into a feminine noun that describes the process or event itself.
Die Austragung des Konflikts erfolgte vor Gericht.
The resolution of the conflict took place in court.
The context makes the meaning clear. If it is about sports, competitions, or events, it means the carrying out or staging. If it is about conflicts, disputes, or disagreements, it means the settlement or fighting out of them.
Die Austragung des Finales wurde wegen schlechten Wetters verschoben.
The staging of the final was postponed because of bad weather.
In a sports context, 'Austragung' (staging) is often connected with specific events such as 'Weltmeisterschaft' (World Cup/world championship), 'Turnier' (tournament), 'Wettkampf' (competition), or 'Finale' (final). A typical verb in this context is 'stattfinden' (to take place).
Die Austragung der Olympischen Spiele ist eine große Ehre für das Gastgeberland.
The staging of the Olympic Games is a great honor for the host country.
When it is about conflicts, 'Austragung' (resolution) is often further specified by adjectives that describe the type of confrontation. Typical examples are 'gerichtliche' (judicial), 'friedliche' (peaceful), 'öffentliche' (public), or 'gewaltsame' (violent) Austragung.
Beide Parteien einigten sich auf eine außergerichtliche Austragung des Streits.
Both parties agreed on an out-of-court resolution of the dispute.
organization
'die Organisation' and 'die Austragung' can both occur in connection with events. 'Organisation' mainly means planning and preparation: rooms, dates, people, and materials. 'Austragung' more often means that an event is actually carried out, especially in sports competitions. So you can plan the organization of a tournament long in advance, but the 'Austragung' happens on the day of the tournament. The words are easy to confuse because organization is also needed for an 'Austragung'.

Die Austragung des Finales findet in diesem Jahr in Köln statt.
The final will be held in Cologne this year.
Für die Organisation des Stadtlaufs sucht der Verein noch freiwillige Helfer.
The club is still looking for volunteers to help organize the city run.