Most decisions that matter are not made against nature but against other people who are deciding at the same time, with their own interests, watching you. Game theory is the study of exactly those situations.
Three ingredients
Strip away the detail and any strategic situation has the same skeleton. There are players, the decision-makers. Each has a set of strategies, the options available. And there are payoffs, a number attached to every combination of choices saying how well each player does.
The word "game" is misleading. The framework was built for war, and it is applied to price wars, arms races, evolution, auctions, courtroom plea bargains, and how a flock decides where to land. What makes something a game is not that it is playful but that your best move depends on somebody else's move.
Writing one down
A two-player game with a handful of options each is usually drawn as a grid. One player picks the row, the other the column, and the cell where they meet holds two numbers: the row player's payoff first, then the column player's.
This little table is doing real work. It makes the interdependence explicit. Read across a row and you see how the row player's fortune swings on a choice that is not theirs to make.
What rationality means here
Game theory assumes players are rational: each has consistent preferences and picks the strategy that leads to the outcome they most prefer, given what they expect others to do. This is a modelling assumption, not a claim that people are cold calculators. It is a baseline that says what a situation rewards, and departures from it are often the interesting part.
Payoffs need not be money. They are whatever the player values, and that can include another player's welfare. If you would rather split a windfall than keep it all, that preference belongs in your payoff numbers. A model where everyone maximises their payoff is not a model where everyone is selfish; it is a model where everyone pursues what they actually want.
Where it goes
Once a situation is written as players, strategies, and payoffs, you can ask a precise question: what will happen? The rest of this course builds the answer, starting with the most famous game ever written down, one whose conclusion is deeply uncomfortable.