Applying game theory to real-world
problems such as credit card debt
|UM Professor Amanda Dawsey
Two men are arrested by the police and confined in separate rooms. Each is visited and given the same offer by prosecutors: “If you testify against your partner and he remains silent, you will go free and he will receive a 10-year sentence. If you remain silent and he testifies against you, he will go free and you will serve 10 years. If each of you betrays the other, both of you will receive a five-year sentence. Finally, if both of you refuse to testify, each of you will be sentenced to only six months.”
Assuming each man’s only interest is in himself, what should the prisoners do?
Amanda Dawsey knows the answer. The UM economics professor specializes in game theory, a branch of applied mathematics dealing with seemingly insoluble problems of cooperation — or betrayal. The so-called “Prisoner’s Dilemma” is the field’s most famous “game,” but contemporary real-world applications exist everywhere from coalition building in Iraq to the ongoing American mortgage crisis. If you want to know how best to buy holiday gifts, contribute to a community garden, recruit for an athletic program — even suck up to superiors or mastermind a reality television show — Dawsey has the answers.
That these situations cannot only be expressed on paper — a simple chart or diagram will do it — but in fact be “solved” is one of the last half-century’s great advances in mathematics and economics. Its most famous practitioner, Princeton Professor John Nash, was the subject of the Academy Award-winning movie “A Beautiful Mind.”
Dawsey’s task: Advance the field and spread the word, from the floor of the U.S. House of Representatives to the minds of Montana students.
Late last September, the U.S. House of Representatives passed H.R. 5244, the “Credit Cardholders’ Bill of Rights.” Before the vote, bill co-sponsor Rep. Carolyn Maloney issued a white paper citing research in progress by Dawsey and co-author Lawrence Ausubel of the University of Maryland.
The Maloney bill was not enacted by the U.S. Senate, but it appears to have forced the hand of the Federal Reserve to enact new regulations that contain similar provisions. In this way, Dawsey’s research affected not only the House bill, but helped lead to what The Washington Post called “the most significant reform of the credit card industry in decades.”
“Previously I had found evidence that creditors face what’s called a ‘common pool’ problem — when creditors go to collect from a borrower in trouble, in collecting they not only take money from the borrower, they make it less likely other creditors will be repaid,” Dawsey explains. “As a result, more competition among creditors is not necessarily efficient — the benefits to everyone are not maximized.”
While general economic theory extols competition, game theory may teach otherwise.
“When you have competition between creditors, you have an inefficient result because borrowers are bled dry,” Dawsey says. “This is why we outlaw things like debtor’s prison and we have structures like bankruptcy to protect borrowers from overly harsh collection.” After all, if someone is in prison, he or she can’t repay a loan; and if debtors repay one party all they have, no money remains for other creditors.
Dawsey derives her conclusions from a dataset of 50,000 gold card accounts at a large credit card lender.
“What was clear from that data is that the more lenders you have the more likely you are to declare bankruptcy,” she says. “If one person has borrowed from three creditors and another person has borrowed the same amount of debt from a single creditor, the person with a single creditor is much less likely to declare bankruptcy.”
The implication is that multiple creditors each attempt to collect early and aggressively rather than giving borrowers time to repay everyone in full.
Dawsey and Ausubel have defined a term, “informal bankruptcy,” which refers to insolvency without a formal filing of personal bankruptcy. Now, in the credit card data, Dawsey says, “we can observe when people are not repaying their cards for six months but are not legally bankrupt.”
In such cases, as opposed to formal bankruptcies, credit card lenders still have a chance to collect the money owed them. Again, however, competition among lenders leads borrowers to declare bankruptcy sooner, thus stopping collection for everyone.
Because bankruptcy imposes severe costs on everyone involved, Dawsey says, “anything that leads to greater cooperation among the creditors would lead to a more optimal result.” Perhaps counterintuitively, a more lenient credit card collection law could save the entire financial system money. Hence the interest of Rep. Maloney.
“One thing you want to discourage is extremely harsh collection techniques by creditors because it’s only going to exacerbate this ‘common pool’ problem,” Dawsey advises. For example, as is, credit card firms can raise interest rates at will, and, game theory demonstrates, they have the individual incentive to do so at the first sign of any borrower distress. The result is akin to a chicken slaughtered before it could lay eggs — bad for the chicken and worse for the farmer.
The same ideas may extend to the current home loan crisis. “The way mortgages are resold and securitized now, there’s no connection between the borrower and the creditor,” Dawsey says. “In that sense, it may be that they’re less likely to be repaid.”
Also at issue is that home payments are only part of most borrowers’ larger debt loads. “If you declare bankruptcy due to credit card debt, that makes you less likely to repay your home mortgage,” Dawsey says. So, for example, debt consolidation, even at a higher rate of interest, may make more financial sense than first appears.
For economists, game theorists are famously far-ranging in their research, and Dawsey is no exception. While her analysis of credit card debt collection was exciting national politicians, Dawsey joined a UM graduate student in economics, Benjamin Harris, and his adviser, Jennifer Alix-Garcia, in pursuing questions about grassroots political participation in Missoula.
Harris and Alix-Garcia wondered whether people living in a “heterogeneous neighborhood” — that is, one with diverse income levels or educational attainments — were more or less likely to participate politically. Interviewing residents of 680 households door to door, his survey team identified three distinct categories of citizens: those who did not participate at all, those who participated alone by writing letters to the editor or watching local meetings on community-access television, and those who participated in person by attending meetings.
Dawsey’s contribution was a model to explain their answers. Her idea was there would be two reasons so-called heterogeneity would impact the likelihood someone would participate politically. “One was economic — if you’re in a neighborhood where everyone’s the same, you don’t have to participate, because you have the same preferences as everyone else, but if you found yourself far from the mean in the neighborhood, your incentive would be to participate to try to influence the neighborhood in a way that would benefit you,” Dawsey says.
Contrariwise, an identity-centered analysis argued that “the more you are unlike everyone else, the more uncomfortable you find it being around them, which leads to decreased political participation,” Dawsey says.
The team’s conclusions, presented at the 2008 Western Economic Association meeting, neatly reconcile the different theories. While neighborhood income disparities appeared not to affect the degree and kind of political participation, differences in educational attainment decreased the likelihood that residents would participate in person — the identity effect — but increased the likelihood of participating alone — the economic incentive. Where high school dropouts live next to postdocs, in other words, expect smaller community meetings but more letters to the editor.
All this still leaves the prisoners’ fates undecided. In this dilemma, Dawsey says, the hard truth is “regardless of what the other prisoner does, you are better off ratting on your partner.”
Think about it: If you betray your fellow prisoner and he says nothing, you go free. If he betrays you, too, you receive five years instead of the 10 you would have earned with silence.
“The prediction of the model is that both ‘players’ rat on each other, which is insightful, because the result is inefficient from the perspective of prisoners,” Dawsey says. “If they could both agree to be quiet, they’d both be better off.”
Dawsey says her students relish the metaphor — criminals apprehended! — until she changes the terms to one of mutually assured environmental destruction. Simply play the same “game” but replace prisoner with polluter and jail sentence with emissions. The sad result is years of choking smog when everyone could as easily cooperate and breathe free.
“The lesson of game theory is that these equilibria can be morally good or morally bad,” Dawsey says. “Depending on the situation you’re describing, they can leave you feeling really good about the world or really bad.”
As she sees it, her work has two goals. “First, I’m interested in understanding people more fully and promoting public policy that’s going to lead to better results.” For this reason, Dawsey says being cited by Congress has been an early career highlight.
“Because if people make mistakes in borrowing decisions, policy can really have an effect on whether those mistakes lead to another small bump in the road or something completely catastrophic.”
Second, however, she says, she just likes solving puzzles. “I get to teach, create and solve these games,” she says. “That’s nothing but fun to me.”
— By Jeremy Smith
|Dawsey’s research suggests that harsh collection laws favoring creditors actually make them less likely to be repaid.