Article published by José Alberto León Alonso, Consulting Director of Corporación 5, in the May issue of La Gaveta Económica.
Among those people who have contributed to expanding the field of application of social sciences in general, and Economics in particular, one of the most outstanding has been John Forbes Nash, who died four years ago in a traffic accident. Mathematician, Nobel Prize in Economics in 1994 for his contribution to Game Theory and Abel Prize in Mathematics in 2015, considered the Nobel Prize in Mathematics, and his figure gained popularity with the film a wonderful mind, which won four Oscars.
At the age of 21, Nash developed his article on game theory that several decades later would earn him a Nobel Prize. Until that moment in game theory it was considered that in competitive situations when some players won, others lost, it was a “zero-sum” game, but Nash focused on cases of competition where there was possibly mutual gain for all players in various circumstances, giving rise to the concept of equilibrium that bears his name.
Game Theory is an area of applied mathematics that studies optimal strategies as well as the expected and observed behavior of individuals in which each person, before carrying out certain actions, analyzes the way in which other people can respond to their actions. For example, in the case of monopolies and oligopolies there is great difficulty for their members to reach an agreement, either to set the quantities of goods to be produced, or on the prices of the goods they produce, or on the part of the market that each one will appropriate. If it is already complex to define how each of the companies in a duopoly will act, it will be much more complicated in oligopolistic markets, with up to a dozen companies. Nash assumes the confrontation between cooperation and the desire to obtain greater individual benefits, but demonstrates that if economic agents interact with each other, each of them choosing their best strategy taking into account the actions of the others, a point of agreement will be reached, the Nash equilibrium, efficient and optimal for all parties.
For Nash, every negotiation has a solution. It proves that there is always a feasible agreement as long as each player's strategy is the best possible and that all parties know each other's possible strategies. In this way, each party executes its optimal strategy in accordance with the actions of the other parties, since it gains nothing by modifying its strategy if the others maintain theirs.
His theory points the way to using game theory to solve social problems. Thus, it shows how to ensure that the intervention of an impartial agent (or an impartial rule) in any negotiation forces the parties to formulate their demands in such a way that all claims are feasible, that is, that the sum of their claims does not exceed the size of the “pie” to be distributed. Nash shows that by simply introducing a little uncertainty into the problem (for example, “if there is no agreement we all lose”), the solution that will be reached will be the one desired by the impartial agent who designs the negotiation mechanism. This is a pioneering proposal at the time by demonstrating that conflicts of interest can be resolved through impartial arbitrators, rules or institutions.
Nash is considered one of the most brilliant mathematicians of the 20th century, among other things for his progress in the application of mathematical tools to other areas. The letter of recommendation for his acceptance at the age of 20 into the mathematics doctorate at Princeton University was brief but clear: “This man is a genius.” In mathematics, genuinely new, genuinely brilliant ideas don't appear every day. In fact, except in the most advanced mathematics, few topics have entered common knowledge after 1950. John Nash earned a special place in the history of this science for his revolutionary contributions in areas as diverse as game theory, geometry, topology and partial differential equations. The famous Nash equilibrium is applied in fields as diverse as economics, computing, artificial intelligence and evolutionary biology. More recently it has been used in studies on corruption and even in relation to the Greek financial crisis. His life was not ordinary either. Nash himself used his axiom that every problem has a solution when he was diagnosed with schizophrenia at age 30. He was hospitalized on several occasions without the possibility of a cure until he realized that the hallucinations were not real, so he decided to solve his psychiatric problem on his own and learned to live with his hallucinations by completely ignoring them, although they never disappeared.
Four years have passed since this genius left us, and we continue to miss him. It will be because we are short of them.
