Jim:
I wrote: >>So far, Game Theory is more of a way of asking questions than it is a theory (like that of supply and demand) that sometimes gives clear answers that have empirical referents.<<
Gil:>Game theory certainly develops a framework for thinking about certain types of questions, but as the name advertises, it's also a theory that yields explanations and predictions about social outcomes in strategic settings. And it "sometimes gives clear answers that have empirical referents", as in the application of game theory to bargaining situations.<
do you have any examples?
To start, most of the contemporary economics literature on industrial organization.
...
>>For example, if you look at a simple "Prisoners' Dilemma" game, game theory makes no predictions unless a very clear equilibrium concept (such as Nash equilibrium) is assumed, going beyond GT _per se_.<<
>I'd say to the contrary that Nash equilibrium is a core part of game *theory*--specifically, noncooperative game theory--as opposed to game "descriptions". It's the starting point for making predictions in noncooperative strategic settings.<
For those who don't know, Nash equilibrium in GT is the equivalent of "rational expectations" in macroeconomics, i.e., totally unrealistic.[*] It assumes that people know much more about the game's rules (and the other participants) than is possible to know. It only makes meaningful predictions if the game description allows the existence of a unique equilibrium.
Well, let's not go off the deep end here. I said that Nash equilibrium is the *starting point* for making predictions in noncooperative strategic settings, and you've suggested some reasons why it shouldn't be the *finishing point* as well. But, contrary to your suggestion, you can apply the notion of Nash equilibrium without assuming that people have perfect or complete information about the game's rules or the nature of other participants (as seen, e.g., in the concept of Bayesian Nash equilibrium), and it is *definitely* not the case that a game must have a unique equilibrium in order to make "meaningful predictions" (although of course sharper predictions are possible if it turns out the equilibrium in the game in question is unique) (one might, for example, still make predictions about movements in the lower and upper bounds of equilibrium outcomes--which is better than nothing, and certainly at least "meaningful"). And the derivation of multiple equilibria is itself a sort of prediction, which lends insight if one instead presumed there must be determinate outcomes arising from given social situations.
Further, it's hard to see what's so unreasonable about the basic concept of Nash equilibrium, which is the idea that in a noncooperative strategic setting--that is, a setting in which, for whatever reason, participants are able to make binding commitments concerning their behavior--a necessary condition for equilibrium is that no participant would choose to depart unilaterally from the equilibrium outcome. As mentioned above, one can generalize this basic idea to a situation in which information is imperfect or incomplete, or strategic interactions are carried out over time.
If Nash equilibrium is in "the core of game *theory*" then GT is rotten to the core.
Again, I don't see the basis for this extreme assessment. It's a necessary condition, but not necessarily a complete statement of what constitutes a reasonable equilibrium for a particular situation under study. With respect to noncooperative situations (described above), what exactly is wrong with the requirement that an outcome can't be counted as an equilibrium unless nobody has an incentive to depart from (and thus undo) that equilibrium?
On the other hand, if Nash equilibrium is seen as merely an ideal and unlikely situation against which the messiness of reality is compared, then maybe there's hope for GT.
How about, a necessary rather than a sufficient condition, which is how it's generally treated in game theoretic applications. It's not obvious why Nash equilibrium should be considered an "ideal," since, for example, Nash equilibria are often inefficient, and very often inegalitarian.
>As for the point that game theoretic predictions are not always borne out, that's true, but in the absence of a superior alternative, this doesn't necessarily count as an indictment, just an observation that social inquiry is not an easy thing to do. ...<
So we should gather a bunch of left-minded microeconomists to develop an alternative to GT.
Why necessarily an "alternative" to game theory, rather than a "left-minded" refinement or adaptation of game theory? Fundamentally, game theory is based on the recognition that people's actions affect each other, and that people are to some extent conscious of this strategic interdependence. What is it about this basic premise that should be categorically rejected? And what's wrong with the adaptations of game theory that "left-minded microeconomists" like Hans Matthews, Jeff Carpenter, Sam Bowles, and Herbert Gintis have in fact been developing?
One thing that would help is to bring in the macrofoundations of microeconomics rather than flirting with discredited methodological individualism. The rules of a "game" are more than mere microfoundations (since they structure micro interactions rather than being a result of them).
I don't see anything about existing game theory that would categorically dismiss these premises. For example, game theory does not itself prescribe what determines the "rules of the game" in question.
So some sort of theory of how these rules are created in a historical process seems needed. Of course, we'd also need a theory of how individual motivations are determined.
I suspect that most contemporary game theorists would endorse these comments as a general statement. Path-dependency is a typical analytical result in many games that are played over time, and psychologists (Kahneman, e.g.) and economic experimentalists are working toward a more fully elaborated "theory of how individual motivations are determined"
Gil
