Students

We have all been there. You stand in the supermarket, scanning the checkout landscape like a grandmaster surveying a chessboard. You spot it: the short line. Three people, modest baskets, a cashier who looks caffeinated. You commit. Two minutes later, the woman in the “long” line next to you is already paying and leaving. Meanwhile, your cashier has called for a price check on an unscannable item, and the person in front of you is counting out pennies. At that point it no longer feels like bad luck, but like the world is against you. But as it turns out, your frustration isn't just a mood; it’s a fascinating intersection of psychology, social justice, and cold, hard probability.

Imagine you test positive for a test that predicts that you have a rare disease with 99% accuracy. You would worry right? You might think this means you almost certainly have the disease, with only a 1% chance of not having the disease. This seems very intuitive, but is actually completely wrong. If the disease is rare, a positive result from this remarkably sensitive test can still mean that you are almost certainly healthy. This feels impossible at first. How can a test that almost never misses a true case be wrong most of the time when it gives a positive result?

Many decisions depend not only on what we want but also on what we expect others to do. Game theory studies these strategic situations, and one of its most important concepts is the Nash equilibrium, a state where each person chooses their best strategy assuming everyone else does the same. A classic example is the Prisoner’s Dilemma, where two suspects can either cooperate by staying silent or betray each other. If both cooperate, they get a light sentence; if both betray, they receive a moderate sentence; and if one betrays while the other stays silent, the betrayer goes free while the silent one gets the harshest penalty. Even though cooperation is best collectively, both usually betray to avoid the worst outcome, creating a stable but suboptimal result. This illustrates how rational choices can lead to predictable patterns, a concept we observe in many areas, including markets, politics, and social media. To understand this better, we first need to explore exactly what a Nash equilibrium is.

Have you ever watched a tweet go viral and wondered if someone is quietly making money from it? That idea is at the core of “Twitter trading”: turning tweets into data that guide trades.