No major league free agents have put ink on new contracts in the weeks since the official opening of free-agent season, but that's a state of affairs that's unlikely to last. With more than 150 MLB free agents, it makes sense for some players to sign with a new team quickly -- or else risk falling through the offseason cracks as Mark Trumbo did last year.
Free agency is a game of musical chairs, albeit one that tends to be a bit more lucrative than the version you played in kindergarten. Here are some free agents who would be wise to sign sooner rather than later.
Zack Cozart, shortstop

In this space last year, one name I suggested sign quickly was Justin Turner of the Los Angeles Dodgers. It wasn't that either the ZiPS projection system or myself thought that he'd be a poor signing -- ZiPS thought he should flirt with nine figures -- but because there were only a few teams really hunting for a third baseman.
Cozart, while not quite as tempting as Turner was from a performance standpoint, enters a free-agent market in which most of the obvious contenders -- and the large-payroll teams which aren't -- tend to be set at shortstop. Of the teams that made the playoffs in 2017, Arizona and Colorado have the weakest situations, but even Ketel Marte and Trevor Story, the likely starters for those respective teams in 2018 as of right now, profile somewhere around league-average. Cozart's a good player, a three-WAR type, but I'm just not seeing a whole lot of opportunities for him to extract top dollar the longer he stays unsigned.
Jose Bautista, corner outfielder

Bautista was in a similar position last offseason, where he needed to find a team that didn't believe his 2016 was the new normal and doing it before the depth charts filled out.
Last offseason, Bautista ended up waiting until the end of January and this offseason is in an even worse position than last after a 2017 that was worse than 2016. He likely will have to find the perfect home: A one-year spot for a miserly team that needs a DH, and there aren't many spots for those. (Tampa Bay maybe?) If Bautista waits too long for teams like that to fill this spot, he may find himself as a non-roster invitee or in his first year of retirement.
Carlos Gonzalez, right field

Like Bautista, Gonzalez is a declining veteran corner outfielder who ought not to wait for a lucrative deal as that deal is likely not forthcoming. There are plenty of corner outfielders available, and few players saw their value decline in 2017 more than Gonzalez.
While his market would have been underwhelming even after 2016-2017 -- sub-.900 OPS seasons from Coors Field outfielders are not star seasons -- Cargo spent most of 2017 well below replacement level. A hot September somewhat salvaged his seasonal numbers, but there aren't many teams these days that will get overly enthused about a single hot month. If someone offers Gonzalez a one-year pillow contract for $15 million, he should quickly take it.
Greg Holland, closer

If any player comes to regret not accepting the one-year, $17.4 million qualifying offer, I think it'll be Holland. Elite closers will get paid, typically by a large-revenue contender that doesn't want to leave closer questions to chance, such as the Yankees or Dodgers last offseason.
But is Holland that type of closer? I lean toward no on that question. While not every team can sign Wade Davis, I suspect Holland's market will be stronger while teams are wondering if they can win an auction for Davis. If you're going to overspend on a closer, you want one that comes with few risks and both Holland's injury history and walk rate keep him from truly being in Davis's class.
Being an Officially Licensed Closer-Type Reliever Guy(TM) is less valuable than it has been since the role was created, and many of the teams that fail to sign Davis are more likely to ask themselves why they should sign Holland with relievers such as Bryan Shaw or Joe Smith are available, who don't come with the closer surcharge from the reliever dealership.
The second-tier first basemen
In Keith Law's ranking of the top free agents, there are five first baseman in the top 20: Carlos Santana, Eric Hosmer, Logan Morrison, Yonder Alonso, and Lucas Duda.
With Santana and Hosmer perceived as the first baseman "to get" this winter, that leaves a lot of competition between the other three even before talking about the lesser options available, such as Adam Lind or Mitch Moreland. Waiting for the Boston Red Sox to either win or lose the competition for Hosmer and Santana sounds like an incredibly risky strategy compared to trying to land one of the open jobs available right now, such as the Rockies, Mariners and Rays
Jay Bruce, right field
Bruce enters free agency in a better position than he would have been last winter if the Mets hadn't picked up the option, hitting .254/.324/.508 with better defense than he played in the recent past. That was good enough to earn him his first two-WAR season, by Baseball-Reference's reckoning, since 2013.
The problem is that despite having a solid season, there just wasn't a great deal of interest in acquiring his services at the trade deadline, Bruce eventually clearing August waivers and in the end, only fetched a single project A-ball reliever in Ryder Ryan. Only one team can trade for Giancarlo Stanton and only one can sign J.D. Martinez, but I think as a fallback option, Bruce will be in a similar position to Mark Trumbo or Chris Carter last year, finding out that homers -- which is most of what Bruce provides -- are cheap right now.
Jason Vargas, starting pitcher
In one of the 2017's biggest surprises,Vargas spent a half-season pitching like Greg Maddux, going 12-3 with a 2.62 ERA in the first-half of the season and making his first All-Star Game. The second half of the season went, well, worse.
A lot of times, pitchers can claim luck on batting average on balls in play as a culprit of sudden decline, but not in Vargas's case, with his BABIP blowing up to an elevated-but-not-unusual .309 after the All-Star Game. Vargas's walk rate nearly doubled in the second half and for pitchers, large walk rate (or strikeout rate) changes tend to be predictive numbers. Vargas showing he was healthy again was a big deal, but showing that his early-season performance wasn't a fluke will be a major challenge, and Vargas may best be served with signing a quick one-year deal with a team with a top pitching coach, such as the Pirates (Ray Searage), Mets (Dave Eiland), or the White Sox (Don Cooper) -- all teams that ought to be looking for bargain starting pitchers, for differing reasons. For Vargas, finding the perfect situation and hitting free agency after 2018 may be more lucrative than trying to get max dollars right now; Vargas may have won 18 games, but it's 2017, not 1997, and pitcher wins have never been held in lower esteem by decision-makers.