A fistfight, and nothing to do with the author of the same name unless the disagreement chances to be over one of his books*. (Improbable, since they have not yet been serialised in "Playboy".)
A kafka is a little confusing as it usually begins as a fasaria but equally a kafka may be described as a fasaria.
Basically, the event may be divided into four stages.
1. The insult.
Real or imagined, this is the justification for stage two. Discussing politics is an excellent alternative to simple abuse and sports may also serve.
2. The challenge.
Dealt with under fasaria, this is an attempt to scare off the opposing individual whilst assessing the strength of any support they may have before it is too late to back down oneself in the event of personal risk being suspected.
An exchange of blows, shoves or knife thrusts.
4. Astinomia (The police)
Whoever loses, challenger or challenged, paints himself in as pathetic a light as possible to the police so that they can arrest the victor and make him pay for his unacceptable behaviour. (i.e. he won.)
Subsequently one or both will present at the local nosogomieon to exaggerate the degree of their injuries and demand x-rays and admission in the hope that they can pressure the hospital staff into giving them written medical grounds for an ego-revivingly successful court case with lots of compensation or else time off work.
Strange though it may seem, actual episodes of public violence are rare in Cyprus unless you visit sink areas like Ayia Napa in which case since you are seemingly looking for the seedier side of life, then frankly you should not be surprised when you find it or else it finds you.
*Kafka, Franz (1883-1924), Austrian (Czech) Jewish novelist and short-story writer. He is considered one of the most significant figures in modern world literature; the term "Kafkaesque" has, in fact, come to be applied commonly to grotesque, anxiety-producing social conditions or their treatment in literature.