Game Theory and the Nash Equilibrium -- Giving Credit to Braess for His Paradox

I am a huge fan of the magazine The Economist and have been a subscriber for many years. If I have an upcoming long flight then I store up and hoard several issues because I know that I will be engaged reading them and also sometimes educated, but not always.

I have also written Letters to the Editor to The Economist. One was published in 2008 and it had to do with traffic and drivers' behavior in choosing routes.

Over the past few weeks I have especially enjoyed a series in The Economist, which is in 6 parts, entitled: Six big economic ideas.

The fifth column in this series, however, piqued me sufficiently to compose a letter. The column was on:  Game theory: Prison breakthrough - The fifth of our series on seminal economic ideas looks at the Nash equilibrium.

The paragraph that bothered me I have taken a photo of and it is the top one below:

Specifically,  the sentences in it that needed proper acknowledgment are: "Self-interested drivers opting for the quickest route do not take into account the effect of lengthening others' journey times, and so can gum up a new shortcut. A study published in 2008 found seven road links in London and 12 in New York where closure could boost traffic flows."

Hence, I composed a Letter to the Editor, which I emailed on August 25.  Since enough time has elapsed I assume that it will not be published so I am reprising it below:

I was delighted to read your fifth brief in the series on seminal economic ideas which featured the contributions of John Nash, whose work, notably, the Nash equilibrium, as you mention, has informed a wide spectrum of fascinating applications, and has fostered additional research. However, I believe in giving credit where credit is due:  although I was pleased to see you mention transportation networks and what is, in effect, user-optimized behavior, in that drivers selfishly choose their cost-minimizing routes of travel from origins to destinations without considering the impact on society, your article fails to acknowledge the (in)famous Braess paradox paper, which was published in 1968 (much before the study in 2008 that you allude to). Braess, in his paper, which was published originally in German, demonstrated that the addition of a new route can make all travelers in a transportation network worse-off. Because of the fascination with this phenomenon, which also can occur in other decentralized networks, Dietrich Braess, Tina Wakolbinger, and I translated the article from German to English and the translation (with a foreword as to how he made this discovery) was published in Transportation Science in 2005 and is now freely available for download:http://homepage.rub.de/Dietrich.Braess/Paradox-BNW.pdf

And, in honor of both John Nash, whom I have cited in probably close to 100 of my papers, and also to Dietrich Braess, another brilliant mind, below I include photos of them. With me and Braess is Dr. Tina Wakolbinger, who was my PhD student at the Isenberg School of Management, and is now a Full Professor at the Vienna University of Economics and Business in Austria.

And for those of you interested in new developments on the Braess paradox, we have now obtained physical proof of its occurrence in electrical circuits: 

Back to the Vikings in Sweden

I am so looking forward to being back in Sweden later this week as part of my sabbatical!

Perhaps you saw the recent special report, The Next Supermodel, on the Nordic countries in The Economist, February 2-8, 2013 issue. I enjoyed reading the follow-up Letters to the Editor on this report, as well, especially the one  from Jens Baunsgaard from Bornholm, Denmark  that said: SIR – Thanks for a very interesting special report about the Nordic countries. However, I must correct you concerning your cover photo: the Vikings never had horns on their helmets. It was Carl Doepler, working for Richard Wagner, who invented horned helmets for the Nibelungen Ring. The myth has been common since then.

 

As an academic, with associations in this region for over a decade, especially Sweden, I marvel at the visionary perspectives of this region, especially its emphasis on and appreciation of environmental sustainability, which I thought was not noted sufficiently in the special report. As a Visiting Professor at the School of Business, Economics and Law at the University of Gothenburg in Sweden, thanks to an ad in The Economist that I responded to, I continue during my stays there to be transfixed by the trams, trains, busses, much utilized, and the pedestrian walkways under foliage and next to bicycle lanes, and the continuous improvements to the infrastructure, even with seasonal flower plantings. The citizens love the outdoors, their parks and their mobility, so that even the restaurants and cafes provide blankets for customers who wish to dine al fresco.

Every time that I return back to the US I say "Why can't the US be more like Sweden" and the special report provided concrete evidence on how public-private partnerships that support innovations can excel and how people can work and live truly well.

Software Codes, Medical Devices and Cybersecurity or Lack Thereof

Cybersecurity is certainly getting a lot of attention in the media lately, and justifiable so.

At UMass Amherst there have been several initiatives in this area, given interests on, may I say, both sides of our campus (from the Isenberg School of Management located in the southern part of campus to Computer Science and Engineering in the north). I suspect that the campus layout designers thought that we would not collaborate but actually some of the most interesting projects (at least the ones that I continue to be drawn to) are across these schools.

Yesterday, after a morning of working in my office at the School of Business, Economics and Law at the University of Gothenburg, where I am now a Visiting Professor, on what was actually a national holiday in Sweden (and, yet,  several of my colleagues also showed up to work), I picked up the latest issue of The Economist, which included one of my favorite segments -- the technology quarterly.

The article, "When code can kill or cure,"  immediately grabbed my attention and, in the third paragraph, my colleague, Dr. Kevin Fu of the Computer Science Department at UMass was quoted. The article also ended with a quote from Kevin, justifiable so, given the fascinating research that he has been doing in identifying how easy it is to hack into many medical devices.

In fact, Kevin, spoke in our UMass Amherst INFORMS Speakers Series in 2008, the same year that an article that he co-wrote on the topic was published. 

In the article in The Economist, some fascinating facts are highlighted:


1. More than half of the medical devices sold in the US (the world's largest health care market) rely on software.

2. Over 80,000 lines of software code may be needed in a pacemaker.

3. A drug infusion pump may have 170,000 lines of code.

3. An MRI scanner may have more than 7 million lines of code.


I have worked on major projects in industry that have also involved security, but of another kind -- I developed assembly language software for the transiting of submarines. I have written about the importance of coding in the curriculum on this blog.

In medical devices, there are now serious issues of both software correctness and remote accessibility and hacking. Kevin calculates that medical device recalls due to software failures have affected over 15 million individual devices since 2002.  His famous 2008 paper, in turn, demonstrated (and he spoke about this very issue in the presentation that he gave in our Speaker Series), how an implantable defibrillator could be reprogrammed wirelessly and remotely. As he noted in the closing paragraph in The Economist article -- "When a plane falls out of the sky, people notice," "But when one or two people are hurt by a medical device, or even if hundreds are hurt in different parts of the country, nobody notices."

There is a call for a government agency, under the recommendation of the US National Institute of Standards and Technology (NIST) , to have the responsibility for approving and tracking cybersecurity in medical devices. There is also a push from the academic sphere for open source software for such medical applications so that errors can be tracked (but there are then challenges to the regulation).

The more technology advances, the more we need to deal with complexity and vulnerabilities. But now the hardware, that is powered by software, may be residing in our bodies or in our loved ones.

Terrific Media Coverage of the Collective Behavior Symposium at AAAS

My brain is still percolating from all the interesting talks that I attended and people that I met at the AAAS Annual Meeting that took place recently in Washington DC.

I also very much appreciate the excellent coverage of the science at this terrific meeting by the media since it is very important to get the news about exciting and important research out!

The Mathematics and Collective Behavior Symposium at the AAAS Meeting was truly enjoyable to be part of. As for media coverage, an article in Science News, entitled, "Model Copes with Chaos to Deliver Disaster Relief, " discusses our research on the design of supply chains for critical needs products from vaccines and medicines to humanitarian relief supplies as well as our research on the management of perishable, life-saving products as in the case of blood supply chains. It also mentions the work of Iain Couzin, who was a fellow panelist of mine at this symposium. Iain and I first met when we were panelists on the Traffic: From Insects to Interstates panel at the World Science Festival in NYC in June 2009 and we had a fabulous time at that event, as well.

The Economist, in its latest issue, also has coverage of Collective Behaviour (British spelling) in a report on Couzin's research in the article: Follow my leader: A group’s “intelligence” depends in part on its members’ ignorance. The article has a gorgeous photo of fish swimming, since that is one type of animal that his research focuses on, but his movies of animals moving and migrating are truly something to behold.

The Economist on the Data Deluge

The Economist has a special report on the volumes of data that is now being regularly generated with a 2008 study by the International Data Corp (IDC) reporting that about 1,200 exabytes of digital data (equivalent to 10 million copies of The Economist) will be generated this year.

With the world becoming increasingly digital, the analysis of the data, and its aggregation, is expected to bring many benefits to different fields, from healthcare, to government, to the business processes and supply chains, to name just a few. Because of the tremendous amounts of data that are now becoming increasingly available through sensors, mobile technologies, cameras, computers, social networking sites, etc., business intelligence techniques, coupled with analytics, that can yield insights from statistical analyses are becoming very important. The deluge of data is so large that it is starting to overwhelm storage capacities of computers (not to mention the ability of humans to process).

Of course, as the report notes, the IT industry is diving deep into business intelligence and notes such companies as Accenture, IBM, and SAP.

I would have liked to have seen in this special report a greater emphasis given to optimization, although it did mention revenue and yield management. The writeup on the visualization of data was especially interesting to me and it highlighted the classic book, The Visual Display of Quantitative Information, by Edward Tuffe. Those of us who work in network analysis have long appreciated the power of networks to represent and depict numerous systems and phenomena.

Reforming Business Schools

The September 26-October 2, 2009 issue of The Economist has an article on reforming business school education. The article argues that business schools should teach more of economic history (I always tell my students the origins of the ideas that I teach, the context and setting of the ideas, and even hand out some of the original papers in which the ideas and innovations have appeared in). In addition, I bring the material to life by including news and events on topics in my lectures. For one thing, if we know the history as well as the scholarly literature, we won't be reinventing the wheel!

In addition, the article emphasizes that business schools need to change their tone and to foster both scepticism and cynicism. In my field, we always state the assumptions underlying the models that we are using. If the problem at hand satisfies the assumptions, then one brings to task the appropriate tools and methodologies.

The article goes on and states rather stridently that It is worth noting that such scepticism is second nature to the giants of financial economics, as opposed to the more junior propellerheads. It then singles out Professor Andrew Lo of MIT (who, by the way, will be speaking this Friday in our Speaker Series in Operations Research / Management Science at the Isenberg School. His talk is co-listed with the Finance Seminar Series).

According to the article, Andrew Lo, of MIT's Sloan School of Management, was fond of pointing out that in the physical sciences three laws can explain 99% of behaviour, whereas in finance 99 laws can explain at best 3% of behavior.

We can hardly wait to hear Professor Lo's talk on Friday, October 2, 2009, at the Isenberg School. The title of his talk is: Kill All the Quants?: Models vs. Mania in the Current Financial Crisis. Additional information on his talk with abstract can be found here.

Being Thanked in the Top Physics Journal

One of the truly gratifying aspects of being a Professor is having students that have graduated write back and stay in touch. Last semester, one of my former undergrads, who had taken my transportation & logistics class, brought to my attention a paper that had been published in the top journal in physics, known as "Phys. Rev. Letters." What amazed this graduate of our Operations Management program at the Isenberg School of Management was that he understood the material and much of it was familiar. News about this article, entitled, "The Price of Anarchy in Transportation Networks: Efficiency and Optimal Control," [Phys.Rev.Lett. 101,128701(2008)] had gone viral with articles appearing in The Economist, the Boston Globe, and the New York Times.

After reading the article it became clear to me that many references were missing and, in scholarship, it is imperative to do a thorough literature search, which establishes precedence. Towards that end, with my husband, who has a PhD in physics, we wrote a response documenting some of the major relevant milestones in transportation network research that should have been included in the article. The rebuttal was not published but, lo and behold, this week there is an errata by the authors in Phys. Rev. Letters {Phys. Rev.Lett. 102, 049905 (2009)], which thanks us and includes some of our suggested references. We are pleased that the authors now understand that science moves forward by standing on the shoulders of giants.

The original article had also motivated my Letter to the Editor to The Economist.