Ron Chernow, in his biography of Alexander Hamilton, writes:
Duels were also elaborate forms of conflict resolution, which is why duelists did not automatically try to kill their opponents. The mere threat of gunplay concentrated the minds of antagonists, forcing them and their seconds into extensive renegotiations that often ended with apologies instead of bullets.
Put that into plain English: We have a Rubinstein bargaining game where players fail to reach an agreement, thereby eating up more and more of the pie. Each individual plays "chicken" and hopes the other will give in. But when you approach the precipice…ah…chicken becomes an increasingly dangerous strategy. The time horizon is truncated, "hold out" behavior becomes riskier, and perhaps the negative wealth effect brings individuals to the bargaining table. (It is complicated; rising costs may simply make you keener to wait out your opponent. A mutual increase in risk, however, can boost the likelihood of a bargain.) Then the Coase theorem kicks in and players reach a deal.
Of course to enforce this meeting of the minds, the the probability has to be real that an actual duel will result.
I used to think of duels as an inefficient form of signaling, typically with honor at stake. In contrast, this hypothesis may suggest that pre-duel risk generation is set privately at too low a level. The riskier you make things seem with your potential opponent, the more that subsequent would-be duelers will be scared into an agreement.
The hypothesis also suggests why duels have (mostly) vanished, namely because trading and contract technologies have improved (except in ghettos). The signaling hypothesis can predict either an increase or decrease in duels, depending on whether the demand for honor or life rises more rapidly with income.