Game Theory

John Nash (1928-...)

In our life, situations such as setting the price for a particular product, the bargaining between two people, internet auctions, art auctions, are very common. In each of these cases, the goal is always to determine the best strategy to maximize gain and / or minimize losses.

For example, in setting the price of a certain product the seller always wants to maximize its profit. Thus, despite being a monopoly position in the market, he can not set the price it pleases because if he does, he may run the risk of asking such an high price that keep away all demand. And even fewer can do it if he has competitors in the market because he runs the risk of consumers prefer to buy the product at a competitor.

Something similar may apply to trade between two people. To illustrate this case we can take the example of wage bargaining between employers and trade union representatives of the employees of a company. In this case, although employers prefer not to raise wages, or at worst, increase them as little as possible, representatives of trade unions wished otherwise. Which means, in this case, nor may employers go for negotiating for a proposal of this type with a very disadvantageous wage for workers nor unions can demand a very high salary increase, under penalty of an agreement is impossible.

For the case of auctions, the goal is always to sell at the highest price and the goal of those who buy is always buy at the lowest price. In this case, the auction format and the rules to which it complies influence the final result. For example, in an auction, all participants can have access to proposals that are being made by the participants but on the other hand, it may also be the case with anyone having knowledge of the proposals submitted. Surely that is not equivalent to opt for an auction model or another.

It's about this kind of topics that focuses the Theory of Games. The Game Theory is a branch of mathematics really booming these days and we can find these and other examples of their application in situations involving defining the best strategy in such popular games like poker and chess, and in many areas of knowledge as economics, finance, biology, sociology, psychology, physics and anthropology.

This branch of mathematics, though not invented by John Nash (1928 -...) and the claims of its invention is attributed to John von Neumann (1903-1957), he was the expanded and endowed with sufficiently powerful tools to solve real problems in various areas. Your work has an importance such that mathematicians made of Newton and Einstein is to physics as well as for Nash are the biological and social sciences. In 1994 John Nash shared the Nobel Prize in Economics with John Harsanyi and Selten Reihnard.

Noteworthy that many have been awarded Nobel prizes in economics for work in the field of Game Theory. This year, Jean Tirole is an example. He has won for his work on power analysis and market regulation. A very timely and relevant topic.