Quantal Response Equilibrium and the Limitations of Game Theory

February 18, 2015

This feature is part of an ongoing RSF blog series, Work in Progress, which highlights some of the ongoing research of our current class of Visiting Scholars.

During his time in residence at the Russell Sage Foundation, Thomas Palfrey (California Institute of Technology) is writing a book on Quantal Response Equilibrium (QRE) and its applications to the social sciences. Developed by Palfrey and Richard McKelvey, QRE is a game theory concept that is now one of the leading approaches to modeling bounded rationality—the idea that individuals’ rationality is limited by the information they have—in games.

In a new interview with the Foundation, Palfrey explained some of the basic applications of game theory to public policy, and the limitations of those approaches.

Q. What is Nash Equilibrium? How has it been applied to public policy, and what are its limitations?

If we define a game as some sort of interactive behavior between two or more people, then Nash Equilibrium is a solution to a game where there is a stable outcome. In other words, it’s a configuration of choices by all the players that ensures that no player on their own could change their choice and gain anything. It’s very much in line with the economics of incentives, so it’s important when it comes to public policy since a lot of those policies have to do with designing incentives for people or organizations to behave in a certain way.

One of the earliest applications was in nuclear deterrence policy. It doesn’t sound like a very good solution, but the concept of Nash Equilibrium underlies the notion of the strategic policy of mutually assured destruction! If two countries are armed to the teeth with nuclear weapons, the Nash Equilibrium is for neither country to attack the other, because if one attacks, they are both bound to be destroyed. There was a lot of work in game theory that was developed in the 50s and 60s to better understand these kinds of ideas, and there are obviously many other military applications.

Another example of Nash Equilibrium applied to policy is in antitrust policy. The antitrust division of the Justice Department is very concerned about keeping markets competitive. As an example, they carefully review mergers, and use game theoretic analysis to try and make predictions about what would happen if the firms in question did merge. They apply the notion of Nash Equilibrium by asking how the configuration of different firms’ strategies—and in particular, pricing—would change if the companies merged.

Q. What is Quantal Response Equilibrium? What does it clarify about game theory?

One of the practical challenges for game theory—and for that matter much of economics—is that when you actually take the ideas to the field and try to apply them, they don’t always function exactly the way they’re intended to function. That’s where my work on Quantal Response Equilibrium comes in. I’m trying to tailor the notion of Nash Equilibrium to allow for more realistic assumptions about how people will act in strategic settings.

In the simplest terms, Quantal Response Equilibrium is a generalization of Nash Equilibrium that takes into account that people make mistakes. Nash Equilibrium is a model of perfectly rational players making perfectly rational decisions all the time. But in the real world, there are a lot of strategic situations where you’re going to get outcomes that are a lot different than what game theory would normally predict, unless everyone’s behaving exactly right. As we know, somewhere along the line, mistakes could be made. Going back to the example of nuclear deterrence, a failsafe program could fail. For instance, while there are many protections against some insane colonel pushing a button that causes a missile to go off, not all of those deterrents are necessarily going to work, and that’s the main reason why people have historically criticized the nuclear arms race. Quantal Response Equilibrium, on the other hand, takes the possibility of error into account.


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