One of the more amusing parlor games played after a presidential election is figuring out who will get what important position in the next administration.

Will Sen. John Kerry of Massachusetts — the best, most logical choice — replace Hillary Clinton as secretary of state, or will President Barack Obama find someone else now that United Nations Ambassador Susan Rice has taken herself out of contention? Will Obama finally banish the Wall Street cronies from the Securities and Exchange Commission and nominate someone as chairman who has a track record of rooting out bad behavior on Wall Street? Will Jack Lew, Obama’s chief of staff, slide over to Treasury to replace Timothy Geithner, or will Obama make the bolder, wiser move and select Erskine Bowles, one of the architects of a smart budget-deficit-reduction plan?

We will probably have to await the new year or an agreement over the looming $600 billion in spending cuts and tax increases — whichever comes first — to hear Obama’s choices for these plum positions. In the meantime, the leakers, positioners, spinners and prognosticators are out in full force, pushing their favorite candidates in the hope that Obama might take notice.

Another important position in Washington that stands to be filled early in Obama’s second term — but isn’t getting a whole lot of attention at the moment — is the one currently held by Ben Bernanke, chairman of the Federal Reserve. Bernanke’s second, probably final, four-year term ends on Jan. 31, 2014. Obama will have to make the nomination of a new Fed chairman a high priority soon after his Cabinet is assembled.

The usual list of highly qualified candidates to replace Bernanke — including Lawrence Summers, the former Treasury secretary and Harvard University president; Janet Yellen, a current vice chairman of the Fed; and Alan Krueger, the precocious chairman of the White House Council of Economic Advisers — misses the person who probably wants it the most and continues to have Obama’s ear on a regular basis: Geithner.

While many people — understandably — assume that Geithner worked at Goldman Sachs before he became Treasury secretary in 2009, actually he was president of the Federal Reserve Bank of New York from 2003 to 2009, the critical years leading up to and including the financial crisis. He has never worked on Wall Street. By design, the New York Fed has traditionally been the most powerful of the Federal Reserve banks, because of its proximity to the powerful Wall Street banks that it regulates. And Geithner played a major role, along with Bernanke and then Treasury Secretary Henry Paulson, in the bailouts of Bear Stearns Cos., Merrill Lynch, American International Group and in the decision to allow Lehman Brothers Holdings to go bankrupt.

Although Geithner failed to pull the punch bowl away just as the party was getting started — which is what William McChesney Martin, the long-serving Federal Reserve chairman, said was the chief responsibility of a Fed governor in order to avoid the kind of financial crisis we experienced on Geithner’s watch — he does possess a keen understanding of what went wrong.

“As is often the case during periods of rapid change, more significant concentrations of risk were present than was apparent at the time,” Geithner told the Council on Foreign Relations on March 6, 2008, just days before the bailout of Bear Stearns. “Banks and investment banks sold insurance against what seemed like low probability events, but did so at what even at the time seemed like low prices. And on the assets they retained, these same institutions purchased insurance from financial guarantors and other firms that were exposed to the same risks. The crisis exposed a range of weaknesses in risk management practices within financial institutions in the United States and throughout the world.”

Last spring, Geithner told Obama he wanted to leave Treasury as soon as possible and return to New York so that he could rejoin his family, while his youngest child was still in high school. But Obama prevailed on Geithner to stick around.

Expect Geithner to seek a short-term sinecure at a liberal think-tank, such as the Brookings Institution, or to return to the Council on Foreign Relations, or to cash in as an adviser to a hedge fund (as Summers did at D.E. Shaw & Co. after he left Treasury) while he awaits the possibility of getting nominated as Fed chairman. If he is serious about the Fed job, he won’t risk taking an appointment — such as the president of Dartmouth job — that would be hard to leave after nine months.

The prospect of Geithner and Summers — two disciples of Robert Rubin, the former Treasury secretary and an architect of the Citigroup debacle — going head-to-head to replace Bernanke would be the firefight of the century, and could open the door wide enough for Yellen, the dark-horse candidate, to slip through and become the first woman to be Fed chairman. Obama is comfortable with making history, and appointing Yellen would be yet another way to do it. But for now, it’s Geithner who has the president’s ear.

William D. Cohan, the author of “Money and Power: How Goldman Sachs Came to Rule the World,” is a Bloomberg View columnist.