John Nash earned a PhD in 1950 from Princeton with a 28-page dissertation, in which he illustrated a crucial concept in game theory, the Nash equilibrium. The Nash equilibrium is the epitome of elegant simplicity and deep insight, and for this work he was awarded the Nobel Prize in Economics.
Game theory offers a framework to analyze the strategic interactions of two or more decision-makers. In a game, the players choose a strategy that would give it the highest payoff based on what has happened so far; the outcome for each player depends on the decisions of the others as well. A Nash equilibrium is reached when no player can do better (further increase its own expected payoff) by unilaterally changing its own strategy.
A well-known application of the Nash equilibrium is Prisoner’s Dilemma, which famously shows that the outcome based on individual choices made by self-interested parties when communications are impossible is not globally optimal.
The setup of the game is as follows. Two fellow criminals are detained and interrogated in separate prison cells. They each are offered lighter sentences if they defect and thus betray the other prisoner. Of course, they can choose to “cooperate” with the other by not saying anything. If both defect, they get a longer sentence than if neither defects. It turns out that the prisoner’s dilemma game has a single Nash equilibrium with both players choosing to defect, an outcome that is apparently inferior to both cooperating.
