Reading a Payoff Matrix and Finding Best Responses

medium

Learn with your AI

Pick a depth. Each prompt opens in your AI pre-loaded with the lesson. Click a row to preview the prompt.

Or teach me the whole lesson:

Why this matters

A payoff matrix is a boring-looking object until you realise it's how every strategic situation gets compared apples-to-apples. 'Best response' is the first real piece of machinery you'll use on one: given what everyone else is doing, which of my moves is best? Everything downstream — Nash equilibrium, iterated elimination, backward induction — is best response reasoning applied in different settings.

Demo

For a two-player game, Row's best response to Column's strategy $s_c$ is the set of rows that maximize Row's payoff given $s_c$ :

B R_{r} (s_{c}) = \arg \max_{s_{r} \in S_{r}} u_{r}

Reading a Payoff Matrix and Finding Best Responses

Why this matters

Demo

Try it yourself

References