Although the concept was actually not an original idea by Nash (it had been developed previously by French mathematician Antoine Cournot in 1838), it was Nash - a doctoral student at Princeton at the time - who first worked out the equilibrium theory in a useful way in his 1951 doctoral thesis.
The Simplicity of the Nash Equilibrium
While game theory itself is a very complex and difficult undertaking, the basic concept of the Nash Equilibrium is a relatively simple one:
Consider two players competing against each other in some form of "game." A Nash Equilibrium occurs if both players find themselves independently following the absolutely optimum strategy for personal success - a strategy which remains the best, regardless of the other player's strategy.
So, if player A is following this optimum strategy and, for the sake of argument, he happens to be able to "peek" at player B's "perfect" strategy, a Nash Equilibrium only exists if, even with this information, his strategy is still the best.
The Nash Equilibrium, in other words, is a sort of "game theory stalemate." It may seem a bit simplistic in this sense, yes, but it certainly possesses qualities which make it important in the prediction of many elements of market economies.
An Example of the Nash Equilibrium
One of the simplest specific examples of the Nash equilibrium in practice would be that of two individual companies, Company X and Company Y, each of whom are in the business of selling the same item, thus making them competitors.
Now, if these two companies each begin by selling the item at the same price - $5, say - then their market shares might be roughly the same.
Each company, then, might search for a means of finding success over the other company, such as by slightly lowering the price (to $4) in order to gain a higher share of the market. So, from the perspective of both Company X and Company Y, this seems like a winning strategy, for though they will make less money on each individual unit, their sales will increase considerably.
If, however, only Company X decides to lower the price, then Company Y will be faced with a situation where they must either face a large loss in sales or to lower their prices as well, so as to remain competitive. And of course this situation also works in reverse.
So, as should be clear, each of these companies is in a position where, regardless of what the other chooses to do, it would be beneficial for them to lower their price, so as to either gain a higher market share or to remain competitive. The two companies are in a Nash Equilibrium.
Of course situations are rarely as simple as this in the "real world," and Nash Equilibriums are rarely perfect, though they certainly provide a useful tool to economists and mathematicians alike to be able to better understand certain decisions in a market economy.
References:
McCain, Roger. Game Theory: A Nontechnical Introduction to the Analysis of Strategy.
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