RE: Nash equilibrium's relevance
If so, why is Nash's equilibrium used for all sorts of things, such as electricity regulation? (If I remember, the movie mentioned that.) Is it that Nash equilibrium is basically a normative concept and that it's applied to improve the efficiency of electricity regulation (or what not) rather than to be an accurate description of the way the world works? In a nutshell, the answer to this is the reason why Nash's Nobel prize was shared with Harsanyi and Selten. They built on Nash's concept and developed the theory of what happens in game-like interactions under less restrictive assumptions about maximal, universal, recursive rationality. When you allow for certain kinds of departures from rationality, it's actually quite a good descriptive tool. Particularly given that the whole thing in its application to electricity regulation has an element of the circle jerk to it; the regulators employ game theorists to design the regulations, and the companies know this, so they hire their own game theorists to exploit the loopholes, which means that the regulators know that the companies are likely to act in accordance with game theory, so they try to design incentive-compatible regulations ... and so on. dd ___ Email Disclaimer This communication is for the attention of the named recipient only and should not be passed on to any other person. Information relating to any company or security, is for information purposes only and should not be interpreted as a solicitation or offer to buy or sell any security. The information on which this communication is based has been obtained from sources we believe to be reliable, but we do not guarantee its accuracy or completeness. All expressions of opinion are subject to change without notice. All e-mail messages, and associated attachments, are subject to interception and monitoring for lawful business purposes. ___
Re: Nash equilibrium's relevance
Jim writes In the article below, Varian explains Nash equilibrium. As an expert in game theory, he points out that it's not a realistic prediction of how people play most actual real-world games. If so, why is Nash's equilibrium used for all sorts of things, such as electricity regulation? (If I remember, the movie mentioned that.) Is it that Nash equilibrium is basically a normative concept and that it's applied to improve the efficiency of electricity regulation (or what not) rather than to be an accurate description of the way the world works? My take on this is that Nash equilibrium or one of its refinements--e.g. the notion of perfect equilibrium developed by Nash's co-Nobelist Selten--provides a plausible reference point, or starting point, for thinking coherently about social outcomes in which strategic considerations may arise. Although it's doubtful that people are unboundedly (individually) rational, as the theory requires, it's at least plausible that their behavior *approximates* this ideal in many settings. Certain economic experiments have shown, for example, that outcomes approach the Nash prediction as people become more familiar with the game being played. And for what it's worth, the global overfishing problem (see the front-page NYTimes article from a day or so ago) seems in many respects like a classic instance of a suboptimal outcome to a prisoners' dilemma-style problem. Granting that predictions of the simple Nash equilibrium are often not realized in practice, though, it doesn't follow that Nash's basic notion of equilibrium in a noncooperative setting--i.e., each actor seeks to realize some objective given that all other players are attempting to seek their respective objectives--is faulty. It may just need tweaking. One possibility is to abandon the notion of selfish preferences, as eg. Mathew Rabin has done by introducing fairness considerations into individual objective functions. Another possibility is to introduce bounded rationality in decisionmaking (as opposed to imperfect or incomplete information, which has already been done--showing how to deal with the latter was part of co-Nobelist Harsanyi's contribution). Gil (BTW, it seems quite a major theme in orthodox economics -- which puts a lot of value on a strong distinction between normative and positive economics -- that normative and positive matters are all mixed up in an ideologically convenient way. For example, the famous Walrasian (Arrow-Debreu) model is really a normative model, since it is based on all sorts of unrealistic assumptions, including the existence of God (the Auctioneer). But then that model is applied to describe -- and worse, prescribe -- real-world matters.) -- New York TIMES/April 11, 2002 What, Exactly, Was on John Nash's Beautiful Mind? By HAL R. VARIAN So what did John Nash actually do? Viewers of the Oscar-winning film A Beautiful Mind might come away thinking he devised a new strategy to pick up girls. Mr. Nash's contribution was far more important than the somewhat contrived analysis about whether or not to approach the most beautiful girl in the bar. What he discovered was a way to predict the outcome of virtually any kind of strategic interaction. Today, the idea of a Nash equilibrium is a central concept in game theory. Modern game theory was developed by the great mathematician John von Neumann in the mid-1940's. His goal was to understand the general logic of strategic interaction, from military battles to price wars. Von Neumann, working with the economist Oscar Morgenstern, established a general way to represent games mathematically and offered a systematic treatment of games in which the players' interests were diametrically opposed. Games of this sort - zero-sum games - are common in sporting events and parlor games. But most games of interest to economists are non-zero sum. When one person engages in voluntary trade with another, both are typically made better off. Although von Neumann and Morgenstern tried to analyze games of this sort, their analysis was not as satisfactory as that of the zero-sum games. Furthermore, the tools they used to analyze these two classes of games were completely different. Mr. Nash came up with a much better way to look at non-zero-sum games. His method also had the advantage that it was equivalent to the von Neumann-Morgenstern analysis if the game happened to be zero sum. What Mr. Nash recognized was that in any sort of strategic interaction, the best choice for any single player depends critically on his beliefs about what the other players might do. Mr. Nash proposed that we look for outcomes where each player is making an optimal choice, given the choices the other players are making. This is what is now known as a Nash equilibrium. At a Nash equilibrium, it is reasonable for each player to believe that all other players are playing optimally - since these beliefs are actually
RE: Re: Nash equilibrium's relevance
Gil writes ... for what it's worth, the global overfishing problem (see the front-page NYTimes article from a day or so ago) seems in many respects like a classic instance of a suboptimal outcome to a prisoners' dilemma-style problem. They presented the problem of overfishing at UC Berkeley grad school without reference to game theory. Instead, the issue of common property resources was very similar to that of pure public goods. Of course, one can probably interpret these both in terms of game theory... but it may be possible to interpret _everything_ in those terms, in which case GT veers toward being tautological. Granting that predictions of the simple Nash equilibrium are often not realized in practice, though, it doesn't follow that Nash's basic notion of equilibrium in a noncooperative setting--i.e., each actor seeks to realize some objective given that all other players are attempting to seek their respective objectives--is faulty. It may just need tweaking. One possibility is to abandon the notion of selfish preferences, as eg. Mathew Rabin has done by introducing fairness considerations into individual objective functions. Another possibility is to introduce bounded rationality in decisionmaking (as opposed to imperfect or incomplete information, which has already been done--showing how to deal with the latter was part of co-Nobelist Harsanyi's contribution). Game theory-type simulations with actual real-live people (i.e., experiments) have suggested such things as that we reject the economists' canonical assumption that individuals are entirely self-interested: in addition to their own material pay-offs, many experimental subjects appear to care about fairness and reciprocity, are willing to change the distribution of material outcomes at personal cost, and are willing to reward those who do not, even when these actions are costly to the individual. (Henrich, Joseph, Robert Boyd, Samuel Bowles, Colin Camerer, Ernst Fehr, Herbert Gintis, and Richard McElreath. 2001. In Search of Homo Economicus: Behavioral Experiments in 15 Small-Scale Societies. American Economic Review. 91(2) May: 73-78.). JD
Re: Nash equilibrium's relevance
James Devine quotes Hal R. Varian of the NY TIMES: What Mr. Nash recognized was that in any sort of strategic interaction, the best choice for any single player depends critically on his beliefs about what the other players might do. Mr. Nash proposed that we look for outcomes where each player is making an optimal choice, given the choices the other players are making. This is what is now known as a Nash equilibrium. 'Can this contract be made against best defense?' What a stupid question. The opponents never find the best defense. The Hideous Hog
Re: Nash equilibrium's relevance
Again, Phil Mirowski's new book is excellent on this. -- Michael Perelman Economics Department California State University Chico, CA 95929 Tel. 530-898-5321 E-Mail [EMAIL PROTECTED]
RE: Re: Nash equilibrium's relevance
I don't have time to finish this book within this decade, but Mirowsky's MACHINE DREAMS is indeed excellent. It's very well written. It's interesting that he contrasts neoclassical economics (which is anti-cyborg) and the cyborgian orthodoxy. He's absolutely right that economists always quote that Robbinsian self-definition of economics being about allocation of scarce resources among competing ends -- and nowadays do all sorts of economics that doesn't fit under that rubric. JD -Original Message- From: michael perelman To: [EMAIL PROTECTED] Sent: 4/11/02 8:07 PM Subject: [PEN-L:24839] Re: Nash equilibrium's relevance Again, Phil Mirowski's new book is excellent on this. -- Michael Perelman Economics Department California State University Chico, CA 95929 Tel. 530-898-5321 E-Mail [EMAIL PROTECTED]
Re: Nash equilibrium's relevance
Michael wrote: Again, Phil Mirowski's new book is excellent on this. Thanks to Michael's previous reference, I read parts of the book and loved it. I am about to start reading it from cover to cover. One feeling I got from the book is that Nash equilibrium is some kind of a paranoid schizophrenic equilibrium. I would add masochistic to that, especially after watching some fights over the net. If the participants of those fights were not driving some pleasure from that self-inflicted pain, why would they continue doing what they are doing? They don't even realize that they are stuck in a paranoid schizophrenic/masochistic Nash equilibrium because of their love for the idea of non-cooperative rationality. They better realize that to break away from that bloody equilibrium, that is, to destabilize it, they need to make a few cooperative moves before they destroy our psychologies too. Who knows, if they take a few cooperative steps, they will even learn to derive some pleasure from cooperation and possibly help us reach a non-Nash equilibrium where, as Louis Armstrong sings in What a Wonderful World, we all will have a decent place under the sun. For the time being, masochistically yours, Sabri
