Principles of Microeconomics / Unit 9 MIC 0827 worked example, 60 to 90 seconds
Reading a Payoff Matrix
The idea
Given a two-by-two payoff matrix, work in four steps. First, for the row player, compare its payoffs down each column and mark its better choice in each; if the same row wins both, that is its dominant strategy. Second, do the same for the column player across each row. Third, a cell where both players' marked choices meet is a Nash equilibrium: neither would change alone. Fourth, compare the equilibrium with the cell both would prefer, if one exists, and name the gap.
In practice
Worked example: two bottlers each choose to hold output or expand. Both hold: ten million each. One expands while the other holds: fourteen for the expander, four for the holder. Both expand: six each. For the first firm, expanding beats holding whether the rival holds, fourteen against ten, or expands, six against four; expanding is dominant. The same holds for the second. Both expand, six each, is the Nash equilibrium, and both would prefer the ten each they would get by holding.
Where people slip
Compare a player's own payoffs only, never the two players' payoffs against each other. And the equilibrium is where the marks meet, not the cell with the largest total; here the largest total is the cell the players cannot reach.
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