A Beautiful Mind, Game Theory and Chess

Beautiful Mind John Nash Roberto Matta “Chess Player”

GAME THEORY AND THE NOBEL PRIZE

Blog by WIM – Beatriz Marinello

On October 12th 1994 – When the newspapers announced that the Nobel Prize in Economics was shared by John Nash, J.C. Harsanyi and R. Selten in 1994 for their work on Game Theory, many were very surprised.

The relation between making decisions in Economy and making decisions in Strategic Gameswas brought to light. 

Some research was done in the early 1920s, but when John Nash made an astonishing discovery early in his career, this intriguing subject took on a different dimension. 

It was now clear to many that if game theory was applied to other areas, it could generate very important and productive results.

A BEAUTIFUL MIND – THE BOOK AND THE MOVIE:

Many of you are probably familiar with the book A Beautiful Mind based on the biography of John Forbes Nash, Jr., Winner of the Nobel Prize in Economics, 1994 by Sylvia Nasar (1999). 

In 2001, this would go on to become an Academy Award winning movie by Universal Pictures.

Interestingly this movie was directed by Ron Howard whose son used to actively play in Scholastic Chess Tournaments.

The movie shows the life of a mathematical genius struggling with a painful and harrowing journey of self-discovery once he was diagnosed with schizophrenia. He eventually triumphed over this tragedy, and late in life, received the Nobel Prize.

GAME THEORY – A POWERFUL CHALLENGER:

Game Theory emerged as a powerful challenger to the conventional method of examining economics.

The main purpose of game theory is to consider situations where instead of agents making decisions as reactions to exogenous prices (“dead variables”), their decisions are strategic reactions to other agents actions (“live variables”).

An agent is faced with a set of moves he can play and will form a strategy, a best response to his environment, which he will play by. 

Strategies can be either “pure” (i.e. play a particular move) or “mixed” (random play).

A “Nash Equilibrium will be reached when each agent’s actions begets a reaction by all the other agents which, in turn, begets the same initial action. 

In other words, the best responses of all players are in accordance with each other.

Game Theory can be roughly divided into two broad areas: non-cooperative (or strategic) games and co-operative (or coalitional) games.

The meaning of these terms is self evident, although John Nash claimed that one should be able to reduce all co-operative games into some non-cooperative form. 

This position is what is known as the “Nash Programme”.

Within the non-cooperative literature, a distinction can also be made between “normal” form games (static) and “extensive” form games (dynamic).

In the 1970s, John C. Harsanyi (1973) provided a remarkably insightful new interpretation of the concept of a “mixed strategy”. 

Game theory has become increasingly popular among undergraduate as well as business school students.

Combinatorial Game Theory studies strategies and mathematics of two-player games of perfect knowledge such as chess or go (but often either concentrating instead on simpler games such as nim, or solving endgames and other special cases).

An important distinction between this subject and classical game theory (a branch of economics) is that game players are assumed to move in sequence rather than simultaneously, so there is no point in randomization or other information-hiding strategies.

CHESS AND GAME THEORY:

Chess provides an excellent setting for the study and understandings of game theories, which can also be applied to many areas including economics.

Although, for study purposes it’s more practical to use endgame positions, rather than utilizing the entire game.

Chess has a brilliant mathematical and logical structure that makes it a perfect candidate for control studies !

In Chess, part of the experience resides in the strategic conflict between the players whom operate at a highly abstracted level, creating a context for this intellectual contest.

Part of the technique of game design is making strategic decisions; each move is a decision which does not necessarily leave room for the player to guess.  And of course, human factors can have an impact on the outcome of the game, regardless of the position.

Chess has a sort of “Zen” quality of symmetry, equality and fair play.

It is interesting that more recent games of military strategy, such as Risk, and its computer relatives such as Age of Empires and Civilization, utilize an asymmetrical structure in which all players do not start with equal assets.
This technique can tend to enhance the drama of the competition, as well as well as the increase of potential variations.

OPENING DOORS – A CONCLUSION: 

In conclusion, the Game Theory opened the door for new applications to games such as chess.

However, in my view, the value goes beyond the obvious observations.

Advances in technology and changes in human behavior, based on these new realities, are moving human intelligence into other dimensions.

Chess can help us in this advancement, by allowing us to excercise the intellectual muscle, that in a sense may weaken over time with technology’s tendency to facilitate even our most basic functions , such as basic arithmetic, reasoning and problem solving. 

Afterall, isn’t it vital to human cognitive development, that we keep the very organ responsible for such theories as the one discussed today, in top condition?

The game of chess can help enhance the thinking process. In the game, it is one person in front of another, no technology, but, man against man, and the organ behind the game – the brain.

I can see how benefits can be reaped from this type of interaction, we need only look a little closer to see how it has helped many people during their developmental years.

Having said this, it is clear, that chess is offering an outlet for pure, real and meaningful thinking.

Progress in education and knowledge are intrinsically related with the human brain and its activities, and chess, as always, will prevail, providing us with a window into the past and…a door…into the future.

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