Nash Equilibrium Payoff Matrix Guide

A payoff matrix is easier to understand when the best responses are visible. A Nash equilibrium is not the highest total score; it is a cell where neither player wants to move alone.

The Nash Equilibrium Payoff Matrix Lab turns a 2x2 game into a visual payoff map. It marks row best responses, column best responses, pure Nash cells, dominance notes and the mixed strategy point when the indifference equations are valid.

How Pure Nash Works

For each column choice, the row player asks which row gives the highest row payoff. For each row choice, the column player asks which column gives the highest column payoff. A pure Nash equilibrium is where those answers meet.

How Mixed Nash Works

Mixed equilibrium makes each player indifferent between their two strategies. The row player's mix is chosen so the column player is indifferent, and the column player's mix is chosen so the row player is indifferent.

Use Cases

• Teaching game theory without hiding the calculation.
• Checking pricing, launch, negotiation or coordination examples with abstract payoff values.
• Creating a receipt-backed classroom or strategy note without copying private data.

Boundary

This is a compact 2x2 normal-form diagnostic. It does not solve repeated games, dynamic games, bargaining, incomplete information, large strategy sets or real-world behavior guarantees.