Nash Equilibria and Schelling Points
Nash Equilibria and Schelling Points
In the context of game theory, a Nash Equilibrium is a result where neither player has an incentive to unilaterally change their strategy. It is often applied to games where both players move simultaneously or when the usefulness of decision trees is low. For example, let's say my girlfriend and I both lose our cell phones and can no longer contact each other. We both actually prefer to be together at home. However, we both also have a slight preference for working overtime. If we come home and find each other there, it would be great. But if we come home and find ourselves alone all night, it would be the worst outcome.
On the other hand, my girlfriend has a similar desire to be with me, be okay with working overtime, but not be alone at home. In this "game," there are two Nash equilibria. If both of us come home, neither of us would regret it as we would get to spend time together and both achieve the highest utility. This is represented by the outcome (3,3).
My girlfriend might think it's better for me to stay at work since she is at her workplace, and I might think it's better for her to stay at work since I am at my workplace. While both of us might think it would have been better if we had both come home, knowing the other person's action, neither of us particularly regrets our own choice.
A Schelling Point is something special. The most important characteristic of a Schelling Point is that it is unique. For example, the Empire State Building may have been the tallest building in New York at a certain time. Noon is the only time that can be considered "exactly midday" except for midnight when people are expected to be asleep and unable to meet properly. Of course, what is considered special is subjective and depends on the observer. As David Friedman wrote, if two people are separately given a list of numbers 2, 5, 9, 25, 69, 73, 82, 96, 100, 126, 150 and are rewarded for choosing the same number, mathematicians are likely to choose the unique even prime number, 2. Non-mathematicians would probably choose 100. For mathematicians, it appears to be a number that is less unique than the other two exact squares. Illiterate people might choose 69 due to its peculiar symmetry. And people with a preference for numbers for reasons other than mathematical might also choose 69.