In "The Bet," once the wager has been made , are the protagonist and antagonist in conflict?
Interesting question. Most teachers stress the basic conflict types. Man vs man, man vs. society, man vs. nature, and man vs. self are the most basic conflict forms.
At the beginning of the story, I would definitely agree that the banker and the lawyer are in a man vs man conflict. The two gentleman are having a civilized discussion about the best way to end a man's life. I'm not sure why discussing that is civilized, but I digress. The lawyer says that capital punishment is horrible because any life is better than no life. The banker disagrees, and says that life in prison is way less humane.
"The death sentence and the life sentence are equally immoral, but if I had to choose between the death penalty and imprisonment for life, I would certainly choose the second. To live anyhow is better than not at all."
The banker then suggests a friendly little bet.
"It's not true! I'll bet you two millions you wouldn't stay in solitary confinement for five years."
The lawyer not only says yes, but ups the ante to 15 years . . . for no more money. What? I don't get it either.
The story makes it appear that the bet began in earnest the next day at noon. From this point forward, I can't positively say that the lawyer and banker are in conflict with each other anymore. They don't have any contact with each other and their actions in no way affect each other.
However, I don't mean to say that the banker and lawyer are free from conflict. It just isn't man vs. man anymore. Both men are in the man vs. self conflict. The lawyer goes through tremendous mood swings throughout his time.
. . . the prisoner suffered severely from loneliness and depression.
Depression was followed by contentment, then insatiable learning, then a sort of frantic learning, followed finally by a completely jaded attitude with humanity in general.
"To prove to you in action how I despise all that you live by, I renounce the two millions of which I once dreamed as of paradise and which now I despise."
The lawyer decides to forfeit the bet 5 hours early and lose everything, because he just doesn't see the point anymore.
The banker is also not free from conflict. Early on, he doesn't have a care in the world. He's rich. But as time passes, his wealth dries up and he realizes that he will be broke if the lawyer wins the bet.
"To-morrow at twelve o'clock he will regain his freedom. By our agreement I ought to pay him two millions. If I do pay him, it is all over with me: I shall be utterly ruined."
That fact introduces the man vs self struggle within the banker. He can honor his bet and be poor. Or he can secretly murder the lawyer and stay semi-wealthy. The banker opts to kill the lawyer.
So to answer your question in a short, direct manner. Yes, once the bet begins, the two men have conflicts. The conflict is with their inner self though and no longer with each other.