Principles of Microeconomics / Unit 9 MIC 0829 worked example, 60 to 90 seconds
A Game Without a Dominant Strategy
The idea
Some games have no dominant strategy, and then only the Nash idea works. Mark each player's best reply to each choice by the other, as before. If a player's best reply changes with the other's choice, that player has no dominant strategy. A Nash equilibrium is still any cell where both best replies meet; there may be more than one, or none in pure choices. Report every equilibrium found and say why no dominant strategy exists.
In practice
Worked example: two firms choose between two incompatible technical standards. If both pick the first, eight million each; both the second, six each; if they split, two each. For the first firm, the first standard is best when the rival picks it and the second standard is best when the rival picks that: no dominant strategy. Both best replies meet in two cells: both on the first standard and both on the second. Two Nash equilibria, one better than the other, and nothing in the game says which they reach.
Where people slip
Two equilibria is not a mistake; coordination games have them, and history or a first mover often decides. And the worse equilibrium is still an equilibrium: once there, neither firm gains by switching alone, which is why inferior standards can persist.
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