A little on bargaining in fantasy baseball

If you took an introductory economics class in college, you probably considered something like the following situation: There are two kinds of people—those with beer and those with pizza. There is lots of each kind. Everyone acts on his own, caring only about himself and colluding with no one. Everyone has identical tastes and would prefer to have some pizza and some beer, rather than all of one and none of the other. Put them all together in some kind of market place and trades will occur—but at what price? That is, how much beer would it take to get a slice of pizza in this setup (call this the pizza price of beer)?

Leon Walras first solved this problem about 120 years ago by asking himself the following question: Is there a price (say two cans per slice) such that all the pizza guys will be willing to sell just the right amount of pizza that the beer guys demand and vice-versa? This is the familiar equilibrium price at which supply = demand. Well, there turns out to always be an equilibrium price, but then an interesting question arises: Since the equilibrium price depends on how much beer and pizza each person has to begin with and what each person’s tastes are, how do all the people know the equilibrium price before the trading takes place?

Suffice to say, while market equilibria like the one above may help us understand free-agent pick-ups, they are not appropriate for discussing trades between just two players with few goods. Instead of lots of divisible beer, you have indivisible Ervin Santana (all or nothing at all). And instead of pizza, your counterparty has Jermaine Dye. And let’s suppose you’d prefer to have the outfielder and he the pitcher. Each of you stands to gain from a one-for-one trade, but that doesn’t mean you’d do it straight-up.

For instance, you know that your opponent really needs a starting pitcher and that he has lots of outfielders. So even though you’d be perfectly willing to trade Santana for Dye, you might try to see if he’d also be willing to throw in, say J.J. Putz to make the deal happen. Of course, he too knows that you need an outfielder much more than you need Santana and might similarly try to hold out for something extra. So now, this something extra that one of you will get from the other will be a sort of price for the trade. The natural question is: What is this price and what determines it?

In such a situation, we are now in the province of Bargaining Theory (BT). For economists, BT is more a tool used to help explain the outcomes of trades that we observe in real life, rather than a normative tool with which to give advice. But understanding the basics of BT can help you avoid some mistakes.

In the end, important determinants of the price are the relative gains that each of you stand to get from the trade. The key though is understanding that it is the gain over the next best option (the “outside option”) that matters, not the gain over doing nothing. If you don’t trade him Santana, maybe someone else will give him Ricky Nolasco for Dye. In no particular order, the key determinants of each person’s outside option are:

    1. What is the likely next best trade that each of you could make? Can he get Nolasco or Matt Garza or just Randy Johnson? What can you get?

    2. How impatient are each of you? Bargaining can take a while. Both sides make offers and counter-offers and so forth. The side which is more impatient will be willing to pay the little extra needed to make the trade happen sooner rather than later. Dye may be an immediate upgrade for you, but perhaps your counterparty has a decent two-start sub for Santana next week. Patience isn’t a voluntary state of mind. I can’t counsel you to be patient—given the parameters of the situation, you either are or are not.

    3. How much does each of you know about the other’s answers to points one and two? Given two rational players, there is not a whole lot of scope for misinformation. Each of you knows each other’s rosters (and all other players’ rosters), the standings and so forth. However, you may be able to feign a higher outside option, for instance by pretending that you have an alternative trade with a different player in the works. In general, talk is cheap and anything you can fake, your opponent can too. But you may be able to take advantage of some asymmetries. Perhaps you both know that there is another player that is desperate need of a starting pitcher. You may know that that third player doesn’t have anything you’re interested in, but perhaps your opponent does not.

Extra Credit (Ultimatum Game): If you can credibly commit to limited conversation, you may be able to get the upper hand. For example, suppose your league’s trading deadline is at midnight tonight. You can make a once-and-final offer (a.k.a. “take it or leave it”) tonight. Tell your opponent you’re going to bed and you’re not going to make or accept a different offer before the deadline. If it is credible, then you may be able to extract that something extra from him.

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