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Revision to Nash Equilibrium (I)

A review of Nash Equilibrium: The Coatings Industry and a Parallel to Science.

By: M.Sc. Ph.D. Julián A. Restrepo R.*

Dear reader, already in some of my previous writings I have raised questions such as What is the current situation of the paint industry in our market?, where is it going? But in this case I go a little further, and try to delve into the subject, so I will include the role of the technician, formulator and coating designer in the equation. 

This writing must be taken in a reflective sense, since it includes various opinions of the author, but in its most critical feeling, it seeks to analyze the approach that is given in paint companies to product development and innovation, its sustainability over time and the proper use of both human and technical resources. 

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Taking into account for this analysis, a tool of economics and game theory to the so-called Nash equilibrium. This considering an environment that speaks more and more of sustainability, both economically and from an environmental point of view, but at the same time, more aware of a changing and increasingly globalized environment.

A review of Nash's balance
Nash equilibrium is a situation where players have no incentive to change their strategy taking into account the strategy of their opponents. In Nash equilibrium, the strategy chosen by each of the participants of a conflict or game is optimal, given the strategy of the others. 

In other words, we can summarize the Nash Equilibrium in that: 
a) Each player will gain nothing by modifying their individual strategy as long as the others maintain theirs. Thus, each individual is executing the best "movement" he can given the movements of others [1]; 
(b) A change of individual strategy is impossible without a change in overall strategy; 
c) The solution is not the creation of new alternatives for each individual to choose his strategy, but the coordination to use sensibly those that exist. [2]

It should be noted that under the Nash equilibrium you do not necessarily get the highest profit for all players as a whole. It is only true that each one responds optimally to the strategy of the others. In many cases, individuals would like to be able to reach another equilibrium with higher profits, but fail to do so because they face the risk of being betrayed. [3] Thus, a Nash equilibrium does not imply that the best result is obtained for the participants as a whole, but only the best result for each of them considered individually. It is perfectly possible that the result would be better for everyone if, somehow, the players cooperated with each other. [1]

In economic terms, it is a type of imperfect competitive equilibrium that describes the situation of several companies competing for the market of the same good and that they can choose how much to produce to try to maximize their profit. [1] Does your application to the paint and coatings market sound familiar?

Perhaps the best-known example of Nash Equilibrium is the one that occurs in the game called "The Prisoner's Dilemma", which is not a paradox in itself, but a problem within the branch of game theory that can be considered paradoxical: The police arrest two suspects. There is not enough evidence to convict them, however, they are separated into two different cells and offered the same treatment: If one of them confesses and his accomplice does not, the accomplice will be sentenced to 10 years and the whistleblower will be released. If both confess, they will be sentenced to 6 years each. If no one confesses, they can only be locked up for 6 months on lesser charges. The experiment shows that two people will not cooperate, even if it is in the interest of both. [4]

A parallel with science
Great scientists who were ignored: Next, we will briefly review cases of scientific advances that were initially ignored by the scientific community, the humiliations suffered by those who made them known and the extremes they sometimes had to go to be taken into account. [5]

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Hand washing saves lives: In 1847 the 28-year-old Hungarian obstetrician Ignaz Semmelweism managed to discover the infectious nature of puerperal fever, managing to control its appearance with a simple measure of asepsis: washing hands. Semmelweism was an assistant at the first gynecological clinic in Vienna, where puerperal fever wreaked havoc. Shocked, Semmelweism began to gather information and first noticed something key: differences in the frequencies with which the disease occurred between the two maternity wards that existed. In the first room, where students who had contact with anatomical studies on corpses worked, the level was much higher. So he concluded that there was a "cadaveric matter" that was transported by the hands of doctors and students and that generated the disease. 

They then had to start washing their hands, before and after attending and examining their patients and managed to reduce the mortality rate in one year from 12.1% to 1.3%. However, his colleagues did not support him with his theory, he was even threatened. His own head of Obstetrics, was against him and banned the sanitary measure. Very bitter, he left the clinic and began teaching Theoretical and Practical Obstetrics at the University of Pest, in Hungary, managing to apply his method. Currently, hand hygiene is the single most important factor for infection control. [6] 

Analysis: Semmelweism's innovation was not only rejected because of his youth, but because he was an intern doctor who challenged the status quo prevailing at the time.

Gastritis is caused by a bacterium: Until 1979, it was believed that stomach ulcer was mainly caused by stress and its causes were unknown. In the city of Perth, Australian doctors Barry Marshall and Robin Warren, discovered the bacterium Helicobacter pylori, which could live in the stomach and cause ulcers and gastritis. According to his research, it was the cause of nine out of ten gastroduodenal ulcers. This was a great discovery, because if the ulcer was caused by a bacterium, it could be cured with antibiotics. However, the scientific community thought they were completely wrong and nobody believed them, because they thought that stomach acid was too potent for a bacterium to survive. 

In 1994, the National Institute of Health approved that antibiotics were the right treatment to cure ulcers and in 2005, with justice, Marshall and Warren received the Nobel Prize in Medicine. [6]. 

Analysis: Marshall and Warren's innovative proposal was rejected, because at the time of discovery, Marshall was still just an intern and it was unthinkable that a simple intern could cure a disease that affects 10% of the population. Also, there was a location problem: Perth, an Australian city that did not have much scientific fame and although science can be done anywhere, the scientific community is accustomed to great discoveries coming from the main centers of research and studies.

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The existence of "quasicrystals": Until 1981 scientists believed that in all solids atoms were ordered to form crystals following symmetrical patterns that were repeated periodically over and over again. 

Between 1981 and 1983 the Israeli scientist Dan Schechtman worked at Johns Hopkins University (USA) with aluminum alloys and using an electron microscope, he observed a structure that moved away from this configuration and that the pattern of the configuration was not repeated. He thus discovered the phase called icosahedral, which opened a new field of study for quasiperiod crystals (quasicrystals). [7] 

His colleagues, meanwhile, said this was simply impossible and was humiliated and ridiculed by the scientific community. Such was the rejection, that the head of his laboratory the day after the discovery, gave him the crystallographic manual they used, with a post it that said "read it". Two days later he was expelled from the laboratory for being a disgrace to the group. Even another colleague of his, the two-time Nobel laureate, Linus Pauling said publicly that "Danny Shechtman is saying nonsense. There is nothing like quasicrystals, only quasi-scientists." 

But Schechtman went ahead with his theory and finally the laboratories, little by little began to prove him right. He won the Nobel Prize in Chemistry in 2011. [6] 

Analysis: Instead of praise for his extraordinary discovery, Shechtman was met with a wall of disbelief and despite ridicule and rejection, Shechtman persisted in his stance that his results were correct.

But, in addition to these stories we could add an endless list of scientists and researchers, some more famous, who were even some considered crazy: Giordano Bruno, Nicolaus Copernicus, Galileo Galilei, Leonardo Da Vinci, Marie Curie, Isaac Newton, Alfred Wegener, Charles Darwin, Ignacio Semmelweis, Svante Arrhenius, Albert Einstein, Thomas Südhof, among others.

I do not want to lengthen the message too much, but the truth is that the life of these characters is truly stimulating, since they came to be considered rebellious by their colleagues and many of them ended up receiving a Nobel Prize.

Note: The second part of this interesting article will develop the situation of Nash Equilibrium applied in the world of science and the coatings industry.

References
[1] http://en.wikipedia.org/wiki/Equilibrio_de_Nash 
[2] (a) http://inversores.es/la-economia-mundial-esta-en-equilibrio-de-nash/; (b) http://arstechnica.com/
[3] http://economipedia.com/definiciones/equilibrio-de-nash.html
[4] https://elfactorciencia.wordpress.com/2013/02/05/paradojas-cientificas-que-no-conocias/
[5](a) http://www.cuantarazon.com/911652/cientificos; (b) http://www.lavozdegalicia.es/noticia/informacion/2013/02/19/nicolas-copernico-galileo-injusta-condena/00031361264484386590505.htm; (c) https://es.wikipedia.org/wiki/Svante_August_Arrhenius; (d) https://www.biografiasyvidas.com/monografia/galileo/
[6] (a) http://www.eldefinido.cl/actualidad/mundo/559/Cientificos_humillados..._que_tenian_razon/; (b) https://noticiasdeabajo.wordpress.com/2011/03/12/estudios-cientificos-que-han-sido-silenciados-por-la-industria-biotecnologica/; (c) http://www.agenciasinc.es/Noticias/Descubrimientos-que-merecieron-el-Nobel-fueron-antes-rechazados
[7] (a) https://es.wikipedia.org/wiki/Dan_Shechtman; (b) https://es.wikipedia.org/wiki/Cuasicristal

* M.Sc. Ph.D. JULIÁN A. RESTREPO R. Advisor and Technical Consultant in Coatings. [email protected] - Medellin, Colombia

Duván Chaverra Agudelo
Author: Duván Chaverra Agudelo
Jefe Editorial en Latin Press, Inc,.
Comunicador Social y Periodista con experiencia de más de 16 años en medios de comunicación. Apasionado por la tecnología y por esta industria. [email protected]

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