I see your point. Even if killing him would be a neutral result, and not killing him would be a positive, one still would make a sacrifice by shooting.

Good point.

I am not sure if this counts as an argument per se, but several works of fiction have had instances where a time machine moves a small amount into the future, (say 1 second), and always travels to 1 second ahead of the protagonist, and thus is invisible. Wouldn't this just give the protagonist a 1 second head start against the villain?

At a time of t=5, both would be visible and present, but the protagonist would have 5 seconds of action time, but the "clever" villain would only have had 4 seconds.

I have wondered a similar thing about the real-life efficacy of bribery.

I was trying to find a counterexample to the "both parties worse off" part of that definition, but now I believe it is correct. Even in what at first appear to only harm one party, such as blackmail, if carried out, the blackmailer spent his bargaining chip.

However, what about cases such as "If you continue to approach me, I'll shoot"? What is the damage done to the shooting party? Assuming no legal retribution and no moral guilt, no loss of respect in the eyes of others, then is his loss the loss of amunition?