Reading a Payoff Matrix

A payoff matrix is a grid built for exactly two firms with two strategies each, so it has four cells. Each cell holds a pair of numbers, by convention the row player's payoff listed first and the column player's second. The matrix exists because once firms can set their own prices, what one earns depends on what the rival does too. Instead of guessing, you can read off every possible outcome and work out what each firm will actually choose.

To read it without mixing up whose number is whose, pick one player and freeze the other's choice. Look down the column (or across the row) that matches the rival's fixed move, then compare your player's two payoffs across their own choices. Whichever payoff is higher is that player's best response to that particular rival move. Repeat this holding the rival at its other possible move, then do the same exercise for the second player. A cell where both firms are playing a best response to each other is a stable outcome: neither wants to switch alone.

This is why the matrix does not send firms to the cell with the highest combined payoff. Firms are not choosing as a team, they are each maximizing their own number given a guess about the rival, so the outcome can be collectively worse even though individually rational. That gap between what is best for each firm and what is best overall is the same tension that drives deadweight loss and price wars in oligopoly, and it sets up the idea of a dominant strategy and Nash equilibrium that follows this topic.