Imagine a local policymaker trying to pull his district out of an economic crisis. Since his funds are limited, he must decide how best to distribute them to ensure the most successful recovery. Reaching that decision requires him to answer several questions. For example, should he subsidize corporations rather than workers or vice versa? Should one type of industry receive more funds than others? And should the policymaker put greater focus on encouraging new investment than on supporting existing investments?

Those conundrums are not restricted to municipalities. National policymakers faced them in 2009 when they developed the stimulus bill intended to put the economy back on course. At issue was the anticipated behavior of the individuals and organizations, otherwise known as “agents,” that were expected to receive the subsidies.

Game theorists refer to this issue as one of coordination. “Coordination is a situation when, out of selfish motives, you want to do what other people are doing—such as speculating against currencies you want to short when other people are shorting,” says Jakub Steiner, assistant professor of managerial economics and decision sciences at the Kellogg School of Management. “This type of behavior is based on self-fulfilling beliefs.”

Playing a Coordination Game

Interactions among several agents are referred to as a game. It becomes a coordination game when multiple stable outcomes—or equilibria—exist and the agents can coordinate equally well in any of them. “Depositors would play a coordination game when deciding whether or not to withdraw their money from a bank,” Steiner explains. “So would traders when they each decide individually to short a currency.”

The challenge for a policymaker facing an economic crisis is to identify the agents in the game with the most influence on the process of recovery, who are thus most worthy of receiving the bulk of the available funds. A poor choice could result in a coordination failure—what Steiner describes as “an equilibrium that’s individually rational but catastrophic overall, such as a bankruptcy, or everyone investing in what turns out to be a bank run.”

Until recently, little guidance has been available on how to choose the most appropriate agent. “It’s a natural question that’s important now but hasn’t been studied in the past because there hasn’t been a good method of studying it,” Steiner explains. “We have found a simple technical way of doing it precisely,” he continues, referring to a model that he and economist József Sákovics, a professor at The University of Edinburgh, have developed.

Two Basic Criteria

“We derive novel results for large coordination games…that allow us to give policy advice over a wide range of situations,” the two report in their paper on the new model. “In the canonical case of investment subsidization we find that ideal candidates for the subsidy need to satisfy only two criteria: (i) their investment has a relatively large direct impact on the incentives of others, but (ii) they are relatively insensitive to the investment of others.” Steiner puts the model’s message more pithily. “You subsidize those industries with high spillover to other agents,” he says, “and those who don’t care too much about the activity of the others.”

The first criterion is fairly obvious. The second is much less so. Why, after all, should one rely on largely independent agents to lead a team effort to avoid disaster? Explains Steiner, “If you subsidize the insensitive agents, by definition those who are not subsidized are quite sensitive to what other people are going to do. So they’ll be quite excited by the increased economic activity of the subsidized ones. That maximizes the indirect effect of the subsidies.”

To illustrate the power of their model, Steiner and Sákovics cite the way in which shopping mall developers set their rental fees. Typically, they point out, the brand-name department stores that anchor any mall receive large discounts on their rents. “Anchor shops bring in loyal customers who end up shopping at other stores as well; thus their decisions have large impact on the decisions of others,” they write. “At the same time their sales are relatively unaffected by the custom of shoppers derived from other stores—as shown by the similarity of their sales per square feet between regional and super-regional malls.”

A Serendipitous Beginning

Steiner and Sákovics’s approach came about serendipitously. “We were playing around with a set of models without anything practical in mind,” Steiner recalls. “Once we found a way to solve problems we hadn’t solved before, it gave us some mathematical way of solving other problems.”

Generalizing the belief constraints for many players in a coordination game, the two write, “allows us to characterize the coordination outcome and specify the optimal policy for a broad range of payoffs and information structures.”

To develop their model, Steiner and Sákovics relied on two critical concepts, one well tried and the other that they devised specifically to deal with coordination problems. “The risk dominance criterion is an old and important concept,” Steiner says. “It shows that in times of uncertainty, mutual worries can become self-fulfilling.” In other words, people and organizations can coordinate in such a way as to harm all parties. For example, they all might withdraw their money from an otherwise solvent bank in the face of a possible bank run, thereby spoiling the bank’s chances of surviving the run.

The other concept—the belief constraint—“is our technical contribution,” Steiner says. “It recognizes that when you ask groups of people with different incentives how optimistic they are about what will happen, you can’t make everybody completely optimistic; there will always be doubts.” Generalizing the belief constraints for many players in a coordination game, the two write, “allows us to characterize the coordination outcome and specify the optimal policy for a broad range of payoffs and information structures.”

Financial Regulation and New Technology

The model provides guidance on situations well beyond mall rentals. Financial regulation is one arena that can potentially benefit from it. Take, for example, a country in such financial distress that it has frozen all bank deposits but then decides to allow some depositors to withdraw their money to maintain liquidity. “Our model allows us to track how a discriminatory withdrawal policy affects the probability of a run, thus informing the policy discussion,” Steiner and Sákovics write.

Similarly, the model can play a role in a corporation’s introduction of new technology, such as videoconferencing. Typically, organizations seed a group of employees to adopt the technology first, in hopes that they will highlight any technical problems and help to convince coworkers to accept the technology. “Our model can easily be adapted to find the optimal seeding policy,” the pair writes. And in the example of economic crisis withdrawal that opened this summary, Steiner says, “the model gives an idea of whom to subsidize to stimulate the economy.”

Awaiting Experimentation

Steiner emphasizes that he and Sákovics have not applied their model to formal examination. “It’s a theory paper; it hasn’t been tested. As a piece of mathematics it’s a speculative model,” he says. “We don’t know empirically in what domains it works and doesn’t work. It may work equally well or badly. It’s a new model. We’ll have to do experiments to test it. And if the profession finds it sufficiently useful, somebody will test it.”

But before that, Steiner continues, “the model may stimulate public policy discussions.” He envisions such discussions in the continuing disagreements over the stimulus program that the Bush and Obama administrations devised to deal with the effects of the economic meltdown of 2008. “I hope that somebody who knows much more about the details of how the stimulus has been done and how other stimuli may be done in the future may find this model useful in organizing his or her thoughts,” he says. “We hope that it will be a useful tool in the discussion.”

Related reading on Kellogg Insight

Firming Up the Foundations of Game Theory: Elucidating the role of information in strategic interactions

Reward Now, Punish Later: Punishment alone may not change social norms

Recession-fighting Serendipity: Well-timed government spending can blunt economic contractions