Payoff matrices and best responses

Try it yourself

1. For the Prisoner's Dilemma from the last task: what is $BR_r(C)$? What is $BR_r(D)$? Write both down.
2. Construct a 2x2 matrix where Row has a different best response to each of Column's moves. (Any game without a dominant strategy for Row will do.)
3. Construct a 2x2 matrix where neither player has a best response that is the same for both of the other's moves. That's the interesting kind.
4. Pick one of your own matrices and circle the best responses. The cells where both circles coincide are pure-strategy Nash equilibria. (Preview for Module 3.)

Prompt your AI

Use these three in order. Each builds on the one before.

1. Basics & terminology

In plain terms, explain what a 'best response' means in a two-player game. Why is it a set rather than a single move?

2. Why it works (the mechanism)

Walk me through how to compute the best-response correspondence for a 2x2 game, step by step, with a numerical example of your choice.

3. Advanced — application & what's next

If a player's best response is the same regardless of what the opponent does, what have we proven? When would best-response reasoning fail to pick out a unique outcome, and why is that the more common case?

References

• Osborne — An Introduction to Game Theory (Ch. 2)
• Stanford CS-264 — Game Theory lecture notes