Principles of Microeconomics / Unit 9 MIC 0828 worked example, 60 to 90 seconds
The Duopoly Game
The idea
Model a two-firm cartel as the matrix of the last video, with hold output as cooperating and expand as cheating. Show that cheating is each firm's dominant strategy, that both cheating is the Nash equilibrium, and that the cooperative cell pays both more. Then explain the price mechanism behind the numbers: the cheater sells more at nearly the cartel price, the holder loses share, and when both cheat the extra output pushes the price down for both.
In practice
Worked example: the two bottlers agree to hold output and share a monopoly profit of twenty million, ten each. If one quietly expands, it sells more at the still-high price and earns fourteen while the other's sales fall to four. If both expand, the price falls and each earns six. Each firm's best reply to any choice by the other is to expand, so both do, and the cartel's twenty million shrinks to twelve.
Where people slip
The cheater's fourteen depends on the other holding; that is why the cartel cannot rest on one firm's honesty. And the numbers are illustrative; what makes the game a dilemma is only the ordering of the four payoffs.
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