Lecture 1: Introduction: Five First Lessons

What this lecture covers

This opening lecture answers a basic question: what makes a situation 'strategic', and how should you reason about it? Ben Polak defines game theory as the study of settings where your outcome depends not just on your own choices but on the choices of others, distinguishing it from the price-taking and monopoly settings covered in introductory economics. The class plays a grade-bidding game live, which turns out to be a Prisoner's Dilemma, and uses it to build up the vocabulary and reasoning tools the rest of the course will rely on.

By the end you can define a strictly dominated strategy, explain why rational, self-interested choices can still produce a collectively bad outcome, and describe why putting yourself in another player's shoes is essential once payoffs differ across players. This lecture sets up the concepts (dominance, payoffs, strategic reasoning) that later lectures on iterative deletion and Nash equilibrium build on.

Key ideas

• Strategic situation: one where the outcomes you care about depend on actions taken by others, not just your own; perfect competition and pure monopoly are not strategic, but everything in between is.
• Payoffs: numbers representing what a player is trying to achieve; you cannot analyze a game, only its structure, until you know what players care about.
• Strictly dominant strategy: a strategy that gives a strictly higher payoff than another strategy, regardless of what other players do.
• Lesson 1 - never play a strictly dominated strategy: whatever the other player does, the dominating strategy does at least as well.
• Lesson 2 - rational choice can lead to bad outcomes: if all players avoid dominated strategies, the resulting outcome can still be worse for everyone than an alternative they could have reached together, as in the Prisoner's Dilemma.
• Lesson 4 - put yourself in others' shoes: to predict what an opponent will do, you need to reason about their payoffs, not just your own.
• Coordination problem: a game where the best response depends on what the other player does, so no strategy dominates, unlike a Prisoner's Dilemma.

Walkthrough

What strategy means and where it applies (0:02)

Polak opens with administrative points about the filmed course, then defines game theory as the study of strategic situations, contrasting it with the non-strategic settings of perfect competition and monopoly from introductory economics. He notes the field applies well beyond economics, including in political science, law, biology and sport.

The grade game and building the payoff matrix (11:08)

Students played a game beforehand: pick Alpha or Beta, paired anonymously with a classmate, where mismatched choices produce very different grades. Polak records the results as an outcome matrix, then builds the standard game theory notation: rows for the player's own choice, columns for the paired player's choice, and both payoffs listed together in each cell.

Strict dominance and the first lesson (21:19)

With payoffs assigned so that players only care about their own grade ('evil gits'), Polak shows that Alpha gives a strictly higher payoff than Beta no matter what the other player chooses. This leads to the formal definition of strict dominance and Lesson 1: never play a strictly dominated strategy, because the dominating strategy does better in every case.

Prisoner's Dilemma and why rational play can be bad (32:49)

The grade game turns out to have the same structure as the Prisoner's Dilemma. Even though both players avoid the dominated strategy, they land on an outcome that is worse for both of them than if they had cooperated. The class connects this to messy dorm rooms, price competition between firms and the classic two-suspects story, and discusses why remedies like contracts, repeated interaction or third-party enforcement can restore cooperation.

Changing payoffs: indignant angels and coordination (41:58)

Polak reruns the game with payoffs that include guilt and indignation ('indignant angels'). With these payoffs neither strategy dominates the other, and the best choice depends on what the other player does, turning the game into a coordination problem. This demonstrates that payoffs, not just the actions and outcomes, determine what the sensible strategy is.

Mixed pairings and Lesson 4 (49:08)

The class then analyzes cross-type pairings: an evil git against an indignant angel, and the reverse. When your opponent has a dominant strategy, working out that fact tells you how to respond even if you yourself have no dominant strategy. This is used to state Lesson 4: put yourself in others' shoes and figure out what they will do.

The pick-a-number game (1:02:31)

The lecture closes with a second live game: each student picks a whole number from 1 to 100, and the winner is whoever is closest to two-thirds of the class average. Polak works through a worked example on the board and collects student guesses, setting up a puzzle about iterated reasoning that the course will return to.

Before you watch

• No prior exposure to game theory is assumed; this is the first lecture of the course.
• A basic comfort with reading a payoff table (rows versus columns, two numbers per cell) will help you follow the matrix construction.

Check your understanding

1. What makes a situation 'strategic' rather than a standard price-taking or monopoly decision?
2. Using the definition given in the lecture, explain what it means for one strategy to strictly dominate another.
3. Why can rational, payoff-maximizing choices by every player still lead to an outcome that is bad for everyone?
4. How did changing the payoffs from 'evil git' to 'indignant angel' change whether a dominant strategy existed?
5. Why does knowing your opponent's payoffs help you decide what to do, even when you have no dominant strategy of your own?