In failing to sign Yoan Moncada, the Yankees lose a key auction

After months of speculation and rumors, the auction for Yoan Moncada's services has ended and the Red Sox have inked the Cuban phenom for about $63 million in total bonuses and penalties. People had initially blamed Brian Cashman for balking at signing him, until this tweet emerged:

To be clear, it's obvious Cashman wanted Moncada but it seems like he couldn't get Hal to go any higher

— wallace matthews (@ESPNNYYankees) February 23, 2015

This isn't the only story, and it looks like there are conflicting reports as to whether Hal Steinbrenner truly blocked a higher bid:

A source tells me Hal S. was NOT the reason Yankees failed to sign Moncada. Others in org felt it wasn't worth it go above $32m

— wallace matthews (@ESPNNYYankees) February 23, 2015

Well then. According to my initial estimations, Cashman not wanting to sign Moncada would be quite different from Hal Steinbrenner not opening up the checkbook, and that is an important distinction to make. What are the implications, though, of Hal blocking a higher bid? Mathematically speaking, it's pretty ludicrous.

The auction for Yoan Moncada is what is called sealed-bid, first-price auction. What that basically means is that other teams' bids are (allegedly) unknown to all other teams, and each team in the auction submits a bid. The highest bid wins, and then the winner pays that amount. If we treat this type of auction as a game theoretic model, then there is a way to game your strategy for maximum payoff, but that may have been done correctly.

In sealed-bid, first-price auctions, it is a strictly dominant strategy to slightly underbid below your "true value", which we would define as the dollar value the Yankees assign to Moncada. The reason for the underbid is that if we subtract the bid from that estimated dollar valuation, you should get a positive dollar amount. That would generate a surplus value, thus resulting in "winning" the auction. If you overbid for Moncada and overshoot your estimated value, then it results in a negative payoff, or what is also called the "winner's curse".

So, if you bid to that strategic value, the worse outcome is having a surplus value of 0, which would be better than acquiring Moncada for more than you estimated him to be worth. But that's probably not what happened. If Hal did in fact block a higher bid, then we know that Brian Cashman had a higher dollar total than the one he submitted, meaning that his bid should have been somewhere higher, possibly near $65 million in total. If generalized into a graphic, it would look something like this:

As you can see, one can initially see the wisdom in not going over your bid, or even submitting a completely truthful bid, because that is where b_i = v_i, but something above b_i" (the bottom alternate bid) is likely the ideal. Unfortunately, the Yankees bid somewhere near that b_i", a bid that is obviously not a dominant strategy because it guarantees a payoff of 0, while bidding higher (which likely would have been above Boston's offer) would result in winning the auction and gaining maximum surplus value from the acquisition.

This is a pretty simplistic model game theoretically speaking, just because we know that bids are not completely sealed, and there's also a large scarcity of information. This model really depends upon actors creating a "true value" for Moncada, but considering they saw him play in a workout just a few times, that level of information is much more incomplete than seeing him play professionally.

But, the larger point prevails. If Cashman had been totally free to place the bid that he wanted to place (if we make this assumption), then it likely would have been considered an optimal bid for a first-price auction. Being forced to undercut your bid, though, is clearly sub-optimal because the Red Sox now have Moncada. One can find even more useful information regarding auctions here (one can also find the unadulterated graphic), and it can be applied to any type of auction where bids are placed in baseball.

The Yankees clearly have the money and financial might to acquire a player in that dollar range, so seeing the Steinbrenners place a hard cap on bidding is obviously, given this model, a bit illogical. This all under the assumption that Hal did in fact place a cap, which is not obvious, so we may never know the truth. If the front office's dollar value estimation was at all higher than the Red Sox's bid, then this strategy is not only illogical, but largely damaging to the long-term health of the club.