That said, I’m a little less optimistic about the problem of multiple equilibria. The problem is not only the impact upon the models predictions and ability to generate insights, which is as you point out, a problem which can be reduced but not eliminated in some cases. But there is also the issue of subjecting the models to meaningful empirical testing. This is difficult to do in the context of multiple equilibria, folk theorems, etc. While simple price theoretic models also do not solve everything, they inherently offer some important advantages in L&E.

Again, none of this is to say that game theory is not a useful tool to shed some light on strategic interactions or clarify analysis where those effects have gone overlooked. Indeed, it is beyond reasonable dispute that game theory has done exactly that in many instances.

Take predation models. Game theory shows that predation is a credible threat in only a narrow range of circumstances. (See John Lott, Are Predatory Commitments Credible?) This analysis has put the predation doctrine under some pressure and perhaps has contributed to judicial reluctance to find predation defendants liable in many situations. Sure the models don’t answer everything. (Neither do other L&E models, by the way.) But still they’re awfully helpful. Same goes for other applications.

In the end, I suppose that “pathbreaking” is in the eye of the beholder. Perhaps “important” is a less subjective term, and perhaps all would agree that game theory’s contributions to law have at least been that.

Back to my antitrust example. The strategic agency literature has produced hundreds of models where by focusing on the possibility of strategic interaction between say, suppliers and retailers, we’ve learned that just about any outcome is possible in equilibrium depending on the assumptions of the model, the type of competition (e.g. Bertrand v. Cournot), the parties’ information sets, and the magnitude of the strategic effects. So we’ve learned, for instance, that all sorts of vertical restraints can possibly be anticompetitive in some of the many equilibria.

So what are we to make of this? Is this contribution pathbreaking in antitrust? Or in your example, the game theoretic literature tells us that all sorts of settlement equilibria are possible. That’s fine. But did folks think about strategic behavior in the context of settlements and negotiations prior to game theory? What is the contribution of game theory here, precisely? Note: I’m not saying there is none, just trying to pin it down. In the antitrust example, there is certainly a contribution. But there is little evidence that these strategic effects are important in the real world in that particular setting. Perhaps they are empirically more important in the settlement setting.

In any event, I guess my point is that being able to model a problem game – theoretically is different than contributing to our understanding of the problem. I am sure that in each of these applications, game theory contributed something to our understanding. But what? This is certain to vary across fields and across problems where strategic effects will have varying impacts. Which is why I want to focus on specific contributions rather than broad methodological ones.

All of this re-framing the question of mine, I think, does not change your answer that settlement is an area where game theory has had a pathbreaking impact — and so I am writing this more to clarify my line of thought than to take issue with any of your helpful comments.

Valuation is one area of the law where I’m holding out hope for “legal reform in light of game theory.” But it hasn’t happened yet. As I see it, game theory’s contribution, like Coase’s, is an enrichment of the analysis in a wide range of applications. There’s no question that game theory is the most academically advanced way to analyze strategic negotiation, and law is filled with situations requiring strategic negotiation. Just about any litigation or transaction situation is amenable to a game theoretic analysis of each side’s “best response.” And what is law if not litigation and transactions. I don’t think it’s a stretch to say that no L&E analysis of a strategic situation is complete without consideration of the game theory dimension.

I guess what I am trying to get at is whether any specific game – theoretic contribution, i.e. a particular article, has changed that field or changed the law in a particular way to reflect those insights? Maybe I’m asking the wrong question. I dont know. Posner’s 6th edition discusses game theory and lists a few specific applications: predatory pricing, contempt, privilege against self-incrimination, court-agency and court-legislature games, blackmail, and law-clerk hiring. Has game theory produced a pathbreaking understanding in any of these areas? The most hopeful candidate, I would guess, is the public choice literature.

Again, using predatory pricing analysis as an example, I dont think that game theoretic insights have been pathbreaking in this area but that is open to some reasonable dispute I would gather.

I’m very interested in your thoughts on this and thanks for your patience while I try to pin down exactly what I am asking!

And Happy New Year!

Josh: Game theory has a wide range of legal applications beyond predation models in antitrust(such as the strategic interactions between litigants or parties to a contract). Posner’s intro to the ’98 edition discusses the broad range of contributions that game theory as of then had made to the law.

The application with which I am most familiar (because of my own contributions in the area) is the recent literature on strategic interaction among valuation litigants, which relies heavily on game theory. But there are many others.

Keith, I wonder what the next revision of Posner, or the one after that, will say about the legacy of game theory in law and economics? In antitrust, for example, the best one might say is that game theory has had a marginal impact on the field. But that does not mean its introduction to other areas of the law would not qualify as pathbreaking. Do you have any specific game theoretic contributions in mind in addition to Baird, Gertner, Picker?

A good way to detect pathbreaking developments in L&E is to look at the key changes Posner makes to his treatise in each new edition. For example, when the fifth edition came out in 1998, Posner emphasized in his introduction that the major change since the last edition was to incorporate the new literature on game theory.