For job seekers, it never rains—it pours. Weeks or months of hunting yield nothing, but then a pair of companies express interest in hiring you—at the same time. But only one of them has made you an offer. Dealing with both, assuming you want both positions, can be like playing two hands of poker at two tables at the same time—but with only one pot to win.
Don't play games
If you find yourself facing this situation, your best path begins with remembering that it is not a game. And the people you are dealing with will appreciate you more if you do not treat it as a game, but instead as the professional negotiation that it is.
Your first move should be to communicate, quickly. Don’t disappear into a bunker and ponder; it’s time to act. Once you have the first offer in hand, call that company and let them know you are definitely interested and would like time to consider their offer. Ask for a date that you can get them an answer. In all but the most unusual circumstances, you should get anywhere from three days to a week. Don’t ask for any more than that. How much thinking does anyone need to do?
Let the other company know you received an offer
Then, immediately speak with your contact at the other company where you are expecting an offer and let them know you’ve received a competitive offer and that you need to give them an answer quickly. Tell this second company that they are your preferred choice, and ask where you stand, and if the process could be expedited. Far more often than not, they will appreciate your candor and work to accommodate in whatever way they can. Sometimes, particularly with larger, less flexible organizations, they cannot.
If the second company cannot accelerate their process, you at least have the power of deciding whether to turn down the offer from the first company without any assurance from the second, or take the "bird in the hand." Best case: you obtain offers from both companies and can compare them side by side to determine which is best for you.
Withdrawing an accepted offer is not preferred
Accepting the first job while waiting for the second offer, and then withdrawing your acceptance to take the second offer is not a preferred method—if you value your reputation. The world is small, and the financial industry is smaller still. You’d be remembered, and not in a positive way.
Following the recommended process, you can rest easy knowing you did what you could, obtained all the info you could get and that you treated everyone fairly and honestly. You’ll be appreciated for you professional behavior. And your reputation will be enhanced, not harmed.