Each firm's profit depends on what its rival does

Two supermarkets share a town. Each must choose to keep its prices high or cut them, without knowing what the other will choose. If both keep prices high, each earns £10 million a year. If both cut, each earns £4 million. If one cuts while the other keeps prices high, the one that cut wins customers and earns £15 million, and the other earns only £2 million. A table of these four outcomes is a payoff matrix.

Cutting prices pays whatever the rival does

Look at it from the first supermarket's side. If its rival keeps prices high, cutting earns £15 million against £10 million for holding. If its rival cuts, cutting earns £4 million against £2 million for holding. Either way, cutting pays more. The rival faces the same choice and reaches the same answer, so both cut.