Some thoughts on auction theory as it pertains to the bidding for Pedro (hey, I was an ec major, I might as well put it to some use). This was my post (in slightly modified form) on SoSH in response to another poster’s idea of requiring that all teams making contract offers to free agents to do so in writing to the player and the agent, in effect making all the various contracts being offered explicit rather than rumours:
The current system of trying to get a free agent to sign makes teams rely on guessing other bids, which is in effect a first-price, sealed-bid auction for the FA’s services, as opposed to the more familiar open auction, which the original proposal.
It may be frustrating to compete in the sealed-bid format, and certainly eBay, or, preceding that, the Sotheby’s-style art auctions, are some well-known auctions, and these are open-auction in format. However, there are good economic arguments for both kinds of auction design. The economist William Vickrey argues that the two should return equivalent results; however, this depends very strongly on a set of assumptions that does not hold in many markets, including that for a baseball player.
One of the main problems associated with an open auction is the possibility of collusion. A recent Athey, Levin, and Seira paper comparing auction designs notes that the potential effects of bidder collusion can well dwarf the relatively minor efficiency effects of an English auction. Collusion doesn’t have to arise overtly, but can also arise tacitly. Since there are different players up for auction (Pedro, Pavano), an open auction would allow buyers to signal to each other who “should” win the bids for each player. (eBay is somewhat insulated from the effects of potential collusion in that eBay has relatively costless entry into the auction. Same goes for the stock market - hard for all the buyers to collude. In Major League Baseball there can only be 30 entrants - plus the odd Japanese team here and there - entering any auction for a player.)
Moreover, open auctions tend to create incentives for stronger bidders to deter weaker entrants through aggressive bidding; you could read the Sox’s fairly high, publicly known initial offer to Pedro as falling into this category - basically indicating “yeah, you can try to top us, but you’d just be wasting effort since we’ll top anything”.
By comparison, sealed bids attract more entrants into the auction. Regardless of how accurate Will Carroll’s data on the Beltran market was, it does seem more that there are more bidders on Beltran besides the Yankees and Astros, whereas the Sox’s initial offer to Pedro helped wipe out a lot of the competition. This works in favour of the sellers, generating more revenue for the sellers. Which is why players like them and owners don’t, and I tend to side with the millionaires over the billionaires.
Theoretically I think openly putting all the information out there has a minor efficiency advantage, but in a market with limited buyers like baseball, the potential for collusion, tacit collusion, and entry deterrence probably makes for a system in which it is overall most economically efficient to keep with the current practice. “Lying” by agents in the latter format is merely another source of (dis)information on what everyone else is bidding - it would be disingenuous of teams to claim that they trusted the agents completely, and teams accept the imperfect signalling and discount the claims accordingly.
(Another helpful article: What Really Matters in Auction Design, which also makes the point that signalling and retaliation are much harder when bids are somewhat unknown.)
Okay, my ec theory may be a bit rusty, but the basic point - that the Sox’s high, publicly known initial offer to Pedro probably dampened the overall market for Pedro - remains.