This is the whole course in one sitting. Every idea you’ve met — the best response you can always name once you know what the other player is doing, the dominant strategy that beats everything, the Nash equilibrium where nobody has a profitable second thought, the prisoner’s dilemma where a stable outcome is a terrible one, the coordination games with more than one equilibrium and the focal points that pick between them, the mixed strategy that makes you unexploitable by making your opponent indifferent, and the closing lesson that you change outcomes by changing payoffs rather than moralising — shows up here as questions. Hold the through-line in your head: a Nash equilibrium is simply a place where everyone is best-responding at once, so no single player can gain by changing their move alone. Take a breath. There is no going back once you commit — a fitting test for a course about the choices no one wants to unmake.
How this exam works
This is a real exam, not a practice quiz. Questions appear one at a time. Once you submit an answer it is locked for good — there is no going back, no retry, and no restart. Your score stays hidden until the very end. A few questions ask you to select all that apply (read those carefully — partial credit is not a thing here). You need 70% to pass. Ready when you are.
What is a "best response" in a game?
Select an answer to continue.
Big picture
Nash equilibrium, in one picture
- Nash equilibrium
- Best response
- Your highest-payoff move given a specific choice by the other player is a best response, and a move that is a best response to everything is a dominant strategy
- Mutual best response
- A Nash equilibrium is a combination where every player is best-responding at once, so no one can gain by changing only their own move - found where both players' best responses coincide, and dominant play is always Nash but Nash is not always dominant
- Stable is not good
- In the prisoner's dilemma both defect for the unique equilibrium (1, 1) even though both prefer (3, 3), because Nash forbids only profitable unilateral deviations, so an equilibrium need not be Pareto-efficient
- Many equilibria
- Coordination games like the standards game, driving side and the stag hunt have several equilibria, creating the selection problem that focal points (Schelling points) solve through shared salience
- No pure equilibrium
- Matching pennies has no pure equilibrium and mixes 50/50, the indifference principle sets your mix to make the opponent indifferent and unexploitable, and Nash's theorem guarantees every finite game a mixed equilibrium
- Change the game
- To change an outcome, change the payoffs with contracts, taxes, repetition or new players rather than moralising - and stay honest that equilibria need not be efficient, fair, unique or actually reached
- Best response
Key takeaways
You now hold the whole model. A best response is your highest-payoff move given what the other player does; a dominant strategy is a best response to everything. A Nash equilibrium is a mutual best response — a combination where every player is best-responding at once, so no one can gain by changing only their own move — and you find it by the best-response method, marking where both players’ best replies coincide. Dominant-strategy play is always Nash, but Nash is not the same as dominant, and a game can have one equilibrium, several, or none in pure strategies (Nash’s 1950 theorem guarantees at least one once you allow mixed strategies). The prisoner’s dilemma — Defect dominates, so the unique equilibrium (1, 1) is Pareto-inferior to (3, 3) — proves that stable is not the same as good. Coordination games (standards, driving side, the payoff-dominant vs risk-dominant stag hunt) have multiple equilibria and the selection problem, which focal points (Schelling points) solve through shared salience. When there’s no pure equilibrium (matching pennies), you mix — and the indifference principle says you set your mix to make the opponent indifferent, which makes you unexploitable (the penalty kick’s 37.5/62.5 split guaranteeing 65%, not 50/50). Finally, to change an outcome you change the payoffs — contracts, taxes, repetition, reputation, new players and information — not moralising. And stay honest about where the model lies: equilibria need not be efficient, fair, unique, or actually reached by real, boundedly rational people.