In professional sports, free agency is the system under which players without a contract entertain offers from different teams. The player is free to sign the contract of their choice, usually the most lucrative… though occasionally a player may have criteria beyond his yearly salary, e.g. the contract’s length or the value of performance-based incentives. The process gives rise to a bidding war for the player’s services – provided that enough demand exists* – between the owners of the interested teams, resulting in a market that can (usually) be expressed as a simple bipartite graph. The results of free agency in the National Football League thus far are discussed in this article from the San Francisco Chronicle.

If there is only one desirable free agent (or if there is a significant gap in skill separating him from the others) at a given position, then free agency functions like an ascending bid auction. The bids are confidential (prompting comparison to the Vickrey auction that provides an identical outcome), but the “auction” allows for multiple rounds of negotiation. Because the winning team will pay its own bid, each will bid lower than its true value; the player may then apprise the losing teams that they have been out-bid, hopefully prompting them to raise their offers. The winning owner will pay a price incrementally higher than the true value of the second-highest bidder. The most recent benefactor of this sort of monopoly might be New York Jets’ left guard Alan Faneca, formerly of the Pittsburgh Steelers, who this spring became the highest-paid lineman in the NFL by signing a contract worth $40 million over 5 years.

If there are several available players of similar ability (as was the case at wide receiver this year after the New England Patriots re-signed Randy Moss; Bernard Berrian and the traitorous Javon Walker headlined a frighteningly inept (and now overpaid) group), then the free agency market can be shown by a bipartite graph that may or may not contain a constricted set. Each “buyer” (i.e. the owner of a given team) has her own value for each player, and each player has some minimum price that they associate with their abilities (so the initial prices are non-zero). Players’ asking prices rise until a set of market-clearing prices is reached; if the owners are rational, then the delay in processing bids/players signing a contract and leaving the market won’t affect the remainder of the bidding process, nor will their order. The scenario differs from those discussed in class because of several outside factors: first, because a player expects a certain amount of money, they can walk away from negotiations; second, there are legal safeguards to protect the players if they end up on the more populous side of a constricted set (allowing them to earn more money than they otherwise would, due to the disparity in supply vs. demand).

* All-time Major League Baseball home run record-holder Barry Bonds does not, evidently, fall into this category