One hundred and fifty years before John Nash received his Nobel prize, a train left Versailles for Paris. On board were two brothers returning home from visiting friends. Always a pleasant journey through the French countryside, this one was, unfortunately, in peril. The train crashed and one of the two brothers, Joseph, was severely injured with a broken bone and other fractures. Joseph Bertrand on that day was 20 years old and was already a professor of mathematics with a doctorate he received at the age of 17 for a thesis in thermodynamics.
Bertrand would later develop a thesis around an economic situation in which two companies dominate a market, formally known as the Bertrand duopoly. He proposed that in a state of duopoly, whereby players offer a non-differentiated product and are not in cooperation, their customers buy from whichever one sells it for cheaper.
Bertrand’s work was one of the foundations upon which Nash would later build. Where Bertrand defined a cutthroat competition, Nash recognized that competitors don’t always know what the other’s cost structure is or what they would do in response to one’s actions, therefore keep making tactical decisions in their businesses resulting in certain payoffs. He stated that there exists a profile of strategies such that each competitor’s strategy is an optimal response to the other’s, there is a point of balance in which neither competitor has anything to gain by changing strategies. That point is called the “Nash Equilibrium.”