Posted without reading the other responses:
Tony - Fired for creating a hostile working environment and being a Grade-A jerk.
Frank - No disciplinary action taken. He tried to resolve the situation properly using the chain of command, but was unable to, through no fault of his own. Punching Tony was regrettable but understandable, under the circumstances.
Mike and Steve - Reprimanded and docked one week’s pay each for not effectively managing the situation before it turned to violence.
I get rid of Tony without question. He’s an abusive shitstain who was actively and deliberately sabotaging my business. Mike goes too, for being complicit in Tony’s douchebaggery and standing by while he sabotaged my business. I apologise to Frank, but ask that in the future he try to take the matter all the way to the top when my managers are failing me and my employees like this rather than resorting to (justifiable) violence. Stephen isn’t at fault - when you’re doing twice your usual workload something’s going to give, and this was no exception.
Then you lack imagination. Words alone can be sufficient justification for violence - if Tony had said he was planning to murder Frank’s wife, for example - and uttering those words in a workplace environment doesn’t diminish that justification.
I’ll give an exception for threats of violence. But that doesn’t apply in this case.
Fire Tony. He was the instigator.
Bullying is not acceptable, fire the bully. He is also guilty of bringing down (or attempting to) the company performance for his own benefit.
The manager needs at the least some training and maybe further disciplinary action.
The guy who threw the punch needs to be let go as well or the bully would have a clear case to take to court for unfair dismissal.
Or you could take the lot to a specialist in remediation and work it out.
Australian view given our HR laws.
Frank has a lawsuit here. Send Frank to anger management classes. Discipline Mike for not taking action and fire Tony for ethics and harassment.
The involved parties can sue regardless of your actions, keeping someone on in hopes they don’t sue you is foolish. Just because they may be happy with an immediate outcome doesn’t mean they can become upset a year later and sue over this incident.
The proper course of action is to follow through with company policy and remain consistent.
Fire Frank. He hit another employee.
Fire Tony. He was clearly harassing a co-worker
Fire Mike. He aware of harassment in the workplace, ignored it and even encouraged it.
Steve employment status is going to depend on what he did or did not know. Had Frank only asked to speak with him? Did Frank say anything to indicate he needed to talk about a serious workplace issue?
If failing to listen to an employee about an unspecified complaint is Steve’s only failing I think he can stick around.
Nothing but a stern talking-to about resorting to violence. Definitely no longer in running for salesman of the year. But an expensive bottle of his favourite hardtack will be in the offing.
Fired so hard his head will spin. Also, if he want to be so gauche as to lay charges, he can kiss any references goodbye.
Fired too. I would not put up with excusing such harrassment shit from any manager of mine.
A good talking-to. The move is a valid excuse for being distracted, but not a great one - he should have still made some time for HR issues.
Fire Tony.
A day’s suspension with pay for Frank, just so people can be truthfully assured he was punished, but we can’t discuss the details of employees’ records due to confidentiality.
A fortnight’s suspension for Mike, as a supervisor. Unpaid.
A shrug for Steve.
This is really a clash of Old School and New School, isn’t it? (Defining Old School as anything older than me and New School stuff youngsters do.)
My BIL, a good ol’ boy from Texas and a marine Vietnam war vet, would fit quite comfortably in that car dealership. He’s figure that Frank did nothin’ wrong, Tony got what he deserved and wonder why Mike would have to be involved anyway. Frank should have punched him when Tony talked trash about Frank’s wife the first time it would have happened.
Some 15 years back when my niece was a toddler, their neighbor’s outdoor cat suddenly scratched her. BIL’s solution was get his gun and shoot the car. Their relationship to the neighbor naturally deteriorated from being good friends to chilly. The neighbor told my sister that she understood the cat needed to be put down, but she would have like to have said her goodbyes and would have had a vet do it.
The old school thought is that you don’t mess with someone’s family.
The problem is that two universes have collided. You don’t to do that anymore. Normally. If this were a fortune 500 company, Mike, Frank and Tony would all be out the door. Steve wouldn’t because it takes more than that to oust upper management.
Although it’s a small company, I still think Mike is too incompetent to keep his job. Even old school managers have to know the limits of their top sales staff. Tony is toast. Donno about Frank. I think he had every right to get angry, but hitting people isn’t cool, no matter what. Maybe a token punishment as others have suggested. I’d have to think more about it. Steve gets away with it because upper management always does.
Fire Frank. Assaulting a coworker is not acceptable. Offer him a generous severance and a glowing reference. If he sues, try to settle with him because we (the company) failed him in allowing a hostile workplace to develop and he has a genuine cause.
Fire Tony, for cause. Harassment is unacceptable and he is an actual menace to our company. Also, douchebag lied about it.
Fire Mike, for thinking the harassment was funny.
Dock Steve’s pay, not enought to blight him eternally, but enough to make him say ouch. Yes, he’s working two jobs at the moment but that’s because he’s expected to handle two jobs. If it was too much for him, he should have proactively told me that things were slipping and asked me for help before he got in the weeds. He should have referred Mike to me if he couldn’t handle it himself. This is no less than I would expect from a person who wasn’t my friend.
Clearly, I screwed up here, too, if harassment was ongoing for a month and I never noticed. In the coming year, I need to get personally involved in making sure that my workplace is a strong and professional team. I need to pay (out of my own pocket, I mean) for better team building opportunities and education so that all of us, top to bottom, have a better commitment to looking out for each other. The good news is, I expect this will pay off with a more motivated and committed workforce as well. But I need to acknowledge that I screwed up here, too.
Aaah, Texas revenge 
*
I’m possibly the biggest pacifist 'round these parts, and even I think that “I’d pay good money to rape your daughter**” is a perfectly understandable example of ‘fighting words’.
I have a daughter who will be 14 in March. I concur that those are an example of fighting words.
I’m no pacifist (I served in the military and have defended myself when attacked abroad), but short of threats of violence, I’m not sure if I see any words (even disgusting remarks about family members) as “fighting words”.
But were I in such a situation, and the management ignored the complaints, then I could quit. Not all people have that luxury, I suppose – if Frank can’t quit, because he and his family really need the money and benefits, then maybe it’s more understandable.
No firings, but Official Reprimands all around. Tony for creating a hostile environment. Frank for assaulting a co-worker. Mike for ignoring the complaints.
Noses will be kept squeaky clean, or the firings begin. If I have a place to move either Tony or Frank, I do so.
Also create an official escalation policy, an “open door” policy with the executives to ensure these complaints do not get missed in the future. With such a policy, Steve would have been on official notice to hear Frank’s concerns.
I was involved in a similar situation several years before I retired. I worked for a large fortune 500 company at the time. One of the mechanics working for me was having an affair with another mechanics wife and bragging about it all over the shop, in graphic detail. The same individual was also a tool thief. He as pure scum. Our branch manager was well aware of the affair and sat around and listened to the scum bag brag about his exploits. He did nothing.
One afternoon at the begaining of our shift I gave the mechanic an assignment and he smarted off to me. Before I even became aware of what I was doing I was kicking his ass. All my resentments toward this guy just suddenly boiled over and I reacted.
I was immediately sent home until firther notice as was the other mechanic. He ended up getting transferred, I got one week off and that was it. Once I explained it to the head of HR in corporate, she took it all the way to the top and it happens our billionaire owner was a good old boy who stated he could afford a lawasuit if it dd happen. I just got lucky. At that time I had 18 good years with the company.I’m 52. Where and when I grew up, there very definitely was such a thing as “fighting words” and the local law enforcement, school administrators, and such acknowledged that, as did the general public. I recognize that the legal environment has changed and that a significant portion of the general public may no longer think that way. However, *I *still think that way. If it is my decision how to handle this, then I will act on my beliefs. The situation is already a shit sandwich. I am not going to force Frank to take a bite just for doing exactly what I would have done in his place.
I suspect the judiciary would still see it that way.
Bunch of Vulcans in this thread…or so you say. There are most definitely fighting words. I don’t have any minors in my care and even I see red at the thought of someone telling me they’d pay money to rape my 14 YO daughter. And yeah, if it had been building on a campaign of harassment, I might pop him one, too.
But I’m only calm as an adult. 
When I was a child and a teen, I had a fine temper. I remember beating up more than one boy bigger than me. The fact that they wouldn’t hit back just meant I could hit them more, in my mind.
Once again, I concur.