By: Megan Mcardle for The Atlantic

Economists would describe hostage negotiation as a bilateral monopoly price negotiation that is structurally just a special case of chicken. That is, unlike a barrel of oil or a freight car full of soybeans which can trade on an extremely liquid market with innumerable buyers and sellers, a hostage has exactly one seller (the kidnappers) and exactly one buyer (the employer and/or family of the hostage). When there is only one buyer, the opportunity cost for ransoming the hostage is zero. Likewise, the employer and/or family has no realistic alternative means to recover the hostage. In order for everybody to walk away happy, we need a cooperate-cooperate outcome: the kidnapper has to give up the hostage and the employer/family has to give up a ransom. This structure also characterizes art theft, which in practice is not a matter of fencing art on the black market but ransoming art to a museum’s insurance company. 

If we model a bilateral monopoly negotiation only two things should matter. The first is, as always in a game of chicken, the willingness to accept failure. The more willing you appear to walk away, the more bargaining power you have. In a more protracted game this can cash out as willingness to delay which we can treat as a defect-defect outcome on the installment plan. In fact in the Planet Money episode on Somali piracy, the hostage’s party did balk and break off negotiations for weeks at a time until the pirates were willing to come down on price.

The other thing that should matter is the capacity to pay. If the pirate knows for an absolute fact that the hostage’s people simply can’t raise more than a million dollars then it would be pointless for them to demand two million dollars. Of course there is an issue of information asymmetry in that the hostage’s party has much better information on its assets than do the pirates and so the pirates may be skeptical of the hostage’s party pleading poverty (especially if the hostage has foolishly told them how much money they can get). We see this at work in the TAL story’s point that kidnapping insurance holds the condition that you can’t tell anyone you have kidnapping insurance.

Here’s something that the econ model tells us shouldn’t matter: the going rate. In normal markets the going rate matters, but only because it provides the opportunities for substitutes and this creates the “law of one price.” For instance, when I go to a grocery store and see a loaf of bread for $4 I won’t buy it. An economist would say I forgo this purchase because I know perfectly well that the going rate for a loaf of bread is about $2.25 and so I can go elsewhere and get bread cheaper. Similarly if I go to the Honda dealer to buy a Honda Accord, it is relevant for me to mention price quotes offered by other Honda dealers for an Accord or even how much Toyota dealers ask for a Camry because it is entirely credible that I’ll walk off the lot and go to rival car dealers offering very close substitutes for this dealer’s cars. However if my sister is locked in a basement in Ciudad Juarez and the kidnappers can credibly commit to not letting her go unless I raise $x, it is completely irrelevant that in the past kidnappers accepted ransoms of $x/2 since I don’t have the relatively good fortune of dealing with a kidnapper who demands $x/2 but am stuck with one who demands $x. There are no other places where I can buy the freedom of my sister and so the only price that matters is the one being demanded by her particular kidnappers. (Note to any cartels reading this: I don’t have a sister).

And nonetheless, much like how most people who haven’t studied statistics balk at the idea that the ratio of sample size to population size is irrelevant to statistical inference, people seem to have a strong intuition that the “market price” is relevant to a bilateral monopoly even though the whole idea of a bilateral monopoly is that there is not really a market but only a series of discrete one-off transactions. In the absence of substitutability, “comparable” transactions are irrelevant as they don’t imply opportunity cost. This is the main thing I found so fascinating about the Planet Money episode, over and over again the hostage’s party balked at the pirates demands as unreasonable in being out of line with the “market price.” We only get the pirates’ story second hand, but apparently at no point did they explain to the hostage’s party that “market price” doesn’t really exist in a bilateral monopoly. (Maybe Mogadishu University needs a better econ department).

There are two ways, which are only partially incompatible, to look at why people insist that there is a market price. The simple model is to see us as making Bayesian inferences about the price the other party is willing to accept. If a pirate asks me for $10 million when I know that previous ransoms for similar hostages from similar pirates were about $1 million, I face two possibilities. It may be that I’m facing an usually greedy or unreasonable pirate and $10 million really is the price from which he will not budge. However it seems more likely that I’m dealing with a regular pirate, who like most pirates in the past will ultimately settle for about $1 million but who is just floating a high initial figure in case I’m especially bad at this. In this sense the distribution of prices for similar transactions may not be directly relevant in the sense of providing opportunities for substitution (or the credible threat to avail myself of them) but it is still relevant as information about the zone of possible agreement. This is consistent with the Planet Money story in that Filipinos are cheaper to ransom than Europeans by an order of magnitude. Presumably this reflects Bayesian inference on the part of the pirates from the hostage’s nationality as to how much the hostage’s party should be able to raise. Alternately we could imagine that pirates always start with the same bargaining position but the Filipinos are less able to pay and so the pirates eventually reach this through ad hoc price discovery on a case-by-case basis. This strikes me as implausible though and I think pirates probably learned pretty quickly what they can reasonably expect for each nationality.

This is a nice explanation and it has the appeal of bending but not breaking the economic model of the actor, but it’s not clear how seriously we want to take it and even if it’s ultimately true it may not reflect the subjective experience. For instance, one of the main explanations for racial discrimination is that it reflects Bayesian inference about aspects of human capital that aren’t readily observable. This model was devastated by Devah Pager’s audit study showing that employers prefer to hire white men with a criminal record rather than black men without a criminal record, whereas the “statistical discrimination” model predicts that ascriptive discrimination should be weaker than and diminish greatly in the presence of information about relevant traits at the individual level. In the wake of the Pager study the best case you can make for the statistical discrimination model is that our intuitions are Bayesian in the aggregate but are too low level for us to override with directly relevant information (or, for that matter, with the conscious desire to avoid stereotyping on legal or ethical grounds). It’s not unlike the argument that evolution made sex feel good so that we will propagate our genes, but it still feels good when you use birth control. So we might prefer a model that is ultimately consistent with people using prevailing price as information in bilateral monopoly negotiations, but is proximately and subjectively more about meaning.

Although the discipline of economics has many valuable things to teach us about how markets work, especially in the long-run, the subjective experience of someone bargaining does not necessarily reflect thinking through how a rational actor would apply price theory (competitive markets) or game theory (monopolistic markets) to the situation. Rather people take moralized approaches to exchange and seem to apply various relational models to exchange, which includes not only market exchange but also gift exchange, patron-client ties, and primitive communism. Moreover, even when people accept that a situation is one of market exchange it does not come naturally to think of price like modern economists think of it, as “market clearing.” Rather much as people intuitively expect physical objects to behave by Buridan’s impetus rather than Newton’s inertia, people’s intuitive notions about price can have less to do with how economics thinks of it than how Aristotle, Aquinas, and Marx thought of it, as “just price” or “fair price.” We see the Aristotelian/scholastic/Marxist understanding of price institutionalized in price controls and laws against gouging. The intuition many people seem to feel is that the long-run prevailing price has moral weight and deviations from this price (as for instance in a supply or demand shock leading to “gouging”) are immoral. Hence historical bread riots often involve not exactly stealing food but rather mobs enacting vigilante price controls. Most recently we saw this is in a class action lawsuit against concession prices in movie theaters. As an American and someone who studies exchange professionally, economics comes naturally enough to me that my immediate reflex to this story is to think this guy needs to understand two-part tariffs and tell him if he doesn’t like the theater’s prices nobody is forcing him to go there or to eat once he arrives. However the fact that somebody felt sufficiently indignant to sue over being offered the opportunity to buy a bucket of popcorn for $6 shows us that the perspective assumed by academic economics doesn’t necessarily come naturally to people. Similarly, when the hostage’s party is negotiating a ransom with pirates both the pirates and hostages may be behaving in ways that are ultimately consistent with a game of chicken under conditions of bounded rationality and Bayesian inference about asymmetric information, but in the immediate subjective sense they may simply be feeling that the recent run of ransoms sets an expectation of what it is fair to pay for this particular hostage.

(Source: youmightfindyourself)