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The Nash Equilibrium provided a new look at certain economic problems and won the Nobel Memorial Prize in Economic Sciences in 1994. Since it's creation, the Nash Equilibrium has been applied to "international relations" specifically for war and arms-race scenarios.
But, has the Nash Equilibrium lead to any significant economic discoveries? I had heard rumors of the Nash Equilibrium being applied to bank-runs and other financial crises but nothing to back it up.

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  • $\begingroup$ In the official Press Release of the Committee, nobelprize.org/nobel_prizes/economic-sciences/laureates/1994/…, the "application of Nash Equilibrium to International Relations", is not mentioned as a reason for the award. Please provide a link for this information, in case I am missing something. $\endgroup$ – Alecos Papadopoulos Dec 15 '14 at 2:45
  • $\begingroup$ Rephrase this to ask if the Nash equilibrium has had any "empirical relevance" and you're golden. As it stands, I think you're probably fine. $\endgroup$ – jmbejara Dec 15 '14 at 3:20
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    $\begingroup$ Following @jmbejara's answer, if you are more generally interested in the empirical relevance of game theory, there is a similar question at math.stackexchange.com/questions/757785/…. $\endgroup$ – Martin Van der Linden Dec 15 '14 at 3:32
  • $\begingroup$ @AlecosPapadopoulos I don't really have any sources. Sorry. I have heard that the Nash Equilibrium has helped provide models for war and arms-race scenarios. I have also heard rumors that the Nash Equilibrium has modeled bank runs and other financial crises, but no hard evidence either way. $\endgroup$ – Mathematician Dec 15 '14 at 18:59
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    $\begingroup$ (+1). Thank you for the cooperative spirit -that's the other important Nash concept - the "Nash bargaining solution"!, en.wikipedia.org/wiki/… $\endgroup$ – Alecos Papadopoulos Dec 15 '14 at 20:05
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Two areas that have been profoundly affected by game theoretic research stemming from Nash's contribution are

Oligopoly theory

There are actually a few examples of what would come to be known as Nash equilibrium in the industrial organization literature that predate Nash's work (for example, Cournot's 1838 analysis of oligopoly competition). However, until Nash (and Selten, Harsanyi, and others) made game theory a general purpose tool, industrial economics was primarily focused on relatively naive models of competition. In the last 30-40 years there has been a revolution in industrial organisation as economists have used game theory to essentially reinvent the study of market competition around oligopoly theory and the study of strategic interaction. Our modern understanding of consumer search, limit pricing, strategic entry and entry deterrance, predatory pricing, strategic advertising, switching costs, product differentiation, platform competition, horizontal and vertical integration, etc. are all predicated on models that rely mostly on Nash equilibrium (or a refinement thereof) as the solution concept. Jean Tirole was recently awarded the Nobel prize largely for work in this area.

This work has also found great practical application in areas such as antitrust policy. Prior to the 1960s, antitrust enforcement in the US (and, to a large extent, elsewhere) was inconsistent and based on unsound economic principles. A combination of the insistence by scholars (especially those based in Chicago) on more careful analysis, and the new tools of oligopoly theory have lead to a much more robust and well-grounded approach to regulating competition.

Auction theory

The study of auctions is game theoretic by its very nature: most auctions involve very direct strategic interaction between a relatively small number of bidders. It should come as little surprise, then, that auction theory essentially did not exist prior to the work of Nash (the formal study of auctions can be traced to W. Vickrey (1961) "Counterspeculation, Auctions, and Competitive Sealed Tenders," Journal of Finance 16(1); also the recipient of a Nobel prize).

None of the cornerstones of auction theory (revenue equivalence, the linkage principle, optimal auctions—source of yet another Nobel prize, etc.) would exist without the solution apparatus that can be traced to Nash. This work, too, has been of great practical importance. From radio spectrum licenses to carbon emissions permits, and from public procurement to Google ad auctions, auction theory has had a significant effect on informing good auction design. See Klemperer (2004) Auctions: Theory and Practice, Princeton University Press for an accessible summary of the theory and its applications.

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    $\begingroup$ One of the reasons that I did not mention auction theory is that it has been shown in a lot of cases that bidders do NOT play Nash equilibria. $\endgroup$ – jmbejara Dec 15 '14 at 20:04
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    $\begingroup$ Add one to your list, perhaps: Climate Change Agreements. If you believe that the world is racing towards 4 degrees Celcius of warming in the next 80-100 years (as all empirical evidence suggests), you could say that game theory will be sadly relevant to the biggest economic disaster in human history; namely, why internationally negotiated climate agreements are either not reached, or why member states just ignore them. Google "game theory of international climate agreements" for lots of rather depressing reading on this. $\endgroup$ – Hexatonic Jan 4 '16 at 2:22
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You're not alone in your skepticism of the relevance of game theory. Some of the greats, including Gary Becker, were at times dismissive of the practical/empirical importance of game theory (see the introduction/preface of his Economic Theory book). No doubt it is in a way foundational to the economic sciences (see Myerson's great essay on Nash's accomplishment, and for other references see this question on math overflow), but there is plenty of skepticism over its empirical importance. For more info and references, take a look at this paper by Chiappori, Levitt, and Groseclose, "Testing Mixed-Strategy Equilibria When Players are Heterogeneous: The Case of Penalty Kicks in Soccer" (American Economic Review, 2002).

The concept of mixed strategy is a fundamental component of game theory, and its normative importance is undisputed. However, its empirical relevance has sometimes been viewed with skepticism.

This paper tries to overcome some of the difficulties associated with formulating a convincing test of the hypothesis that people play mixed strategies. There are plenty of other papers on the topic, but I think this one is relatively well known.

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  • $\begingroup$ Regarding the relevance of mixed equilibria, a similar paper is "Minimax play at Wimbledon" by Mark Walker and John Wooders available at math.sunysb.edu/~gaston/print/Old/WimbledonAER.pdf $\endgroup$ – Martin Van der Linden Dec 15 '14 at 3:55
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This is only half a joke : Nash-equilibrium gives a very good prediction on the relative size of groups of foraging ducks on a pond when two food sources are established at opposite sides of the pond.

enter image description here

A very good explanation can be found at https://headbiotech.wordpress.com/nash-equilibrium-example-on-ducks/, among other places (https://headbiotech.wordpress.com/... is where the image comes from).

In my views, this example illustrates how the Nash-equilibrium solution concept sometimes matches the "steady states" of implicitly dynamic/repeated games.

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  • $\begingroup$ This doesn't seem like a very interesting example because the Nash-equilibrium is the same as the global optimum. Have people done experiments on animals where the two differ? $\endgroup$ – GS - Apologise to Monica May 2 '15 at 7:09
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    $\begingroup$ @GaneshSittampalam : what do you mean by "global optimum"? $\endgroup$ – Martin Van der Linden May 6 '15 at 16:11
  • $\begingroup$ Good question, that's not well defined. I think I really mean that there's no "prisoner's dilemma" type conflict. $\endgroup$ – GS - Apologise to Monica May 6 '15 at 16:14
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Glen Weyl, an economist at Microsoft, in a letter to The Economist, 2016-09-17:

You mentioned the role of Nash equilibrium in redesigning the system of matching job offers at hospitals with medical students. Although a common story, the actual history does not line up as the triumph for non-co-operative game theory you think it is. The “deferred acceptance” algorithm now in use in the system was discovered by medical staff before its rediscovery by David Gale and Lloyd Shapley in the 1960s. In any case, it relies on a co-operative game theory of stability, which is an alternative to Nash’s non-co-operative equilibrium, not an application of it.

Nash equilibrium has transformed the way economists think about their field, but clear practical applications of the concept are harder to pinpoint than they might at first appear. The same might be said of Newton’s theory of gravitation and many other great scientific achievements.

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