I haven't come across the term 'amicable contest' but we have the terminology of 'consensual violence'. Within this context two guys in the pub upset each other and 'agree' to have a dust up, no one is hurt and there is no damage to property, police may well give a verbal warning and use their discretion not to press charges knowing that something minor like that would in all probability be thrown out of court. There is an implied consent even though technically the contest is still illegal.
If in the scenario above one of the guys was not wanting to fight there is no consent and it becomes straight out assault.
Where it gets murky is when two guys agree to fight and one is injured. At law, in many places, there was consent to the fight but there is not consent to the injury. In other words, you agree to fight with another idiot who has also been drinking. You hit him, he falls and hits his head and either dies or sustains life threatening injury. Your 'consent' just disappeared into thin air, go to jail, do not pass Go. Even the fact that one person had been drinking will make 'consent' a very shaky defence.
In other words, getting into any fight unnecessarily is a pretty dumb thing to do.
For anyone with some time on their hands and an interest in law as it may be interpreted in Australia, Canada or the UK ....
http://www.austlii.edu.au/au/journals/UWALawRw/1996/6.pdf