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Markets and auctions
Cournot duopoly
Two firms make the same product and sell it in the same market. Each decides how much to make, and the price is set by the total: the more both make, the lower the price for everyone.
Here the price is 12 minus the total made, and making it costs nothing, so each firm earns its output times the price.
You are Firm 1
Set how much to make for each side, or press a button to make that side play its best reply to the other.
What it teaches
Competing in quantities leaves each firm producing output that its rival would rather it did not, so the market settles strictly between monopoly and perfect competition instead of at either extreme.
The usual mistakeExpecting two firms to land at one of the two familiar extremes, either tacitly splitting the monopoly output or competing the price down to cost, rather than at a point in between that neither firm prefers.
The checkWrite each firm's
best response to the other's quantity and find where the two curves cross. That crossing, not either extreme, is the prediction.
In the real world
Fiction: The Wire
The co-op as an agreement about volume
Proposition Joe assembles a co-operative so that the Baltimore organisations draw on one wholesale connection and stop fighting over ground. The agreement is about volume and territory rather than price: each crew's share is what it may put on the street, and anyone who floods his corners lowers what everyone's product fetches. Marlo Stanfield joins without ever accepting the restraint, and the arrangement does not survive him.
The co-op is an agreement about quantity propping up a price that no single crew sets, so defecting means putting out more rather than charging less, which is what separates it from the corner price war in the same show.
Real worldContested
OPEC+ production quotas
OPEC+ negotiates output quotas rather than prices, and the price is whatever the market pays for the total that results. Each member's extra barrel lowers the price on every other member's barrels, which is the externality the model is built around, so quotas are persistently exceeded and compliance has to be monitored and argued over. When Saudi Arabia and Russia failed to agree on cuts in March 2020 both opened the taps, the price collapsed, and the episode showed what the quantity externality costs when nobody restrains it.
The instrument is quantity and the price is a residual, so there is no undercutting to be done and margins survive; the same producers competing on price with an identical barrel would be driven to the cost of lifting it, which is the Bertrand case.
Next door on the wall
Bertrand duopolyChoosing quantities rather than prices, which leaves both firms with positive margins instead of none. Not on the wall yet.
Common-pool resource gameThe externality falls on fellow users of a resource rather than on rivals in a market, so the identical algebra describes a loss to be prevented rather than a gain to buyers. Not on the wall yet.
Partnership effortThe externality running through a shared payment rather than a market price, so the shortfall is in effort supplied rather than output withheld. Not on the wall yet.
Sources
- Cournot, A. A. (1838). Paris: Hachette. The original quantity-competition duopoly.
- Tirole, J. (1988). MIT Press.