A duopoly (from
Greek , ; and , ) is a type of
oligopoly where two firms have dominant or exclusive control over a market, and most (if not all) of the
competition
Competition is a rivalry where two or more parties strive for a common goal which cannot be shared: where one's gain is the other's loss (an example of which is a zero-sum game). Competition can arise between entities such as organisms, indi ...
within that market occurs directly between them.
Duopoly is the most commonly studied form of oligopoly due to its simplicity. Duopolies sell to consumers in a competitive market where the choice of an individual
consumer choice cannot affect the firm in a duopoly market, as the defining characteristic of duopolies is that decisions made by each seller are dependent on what the other competitor does. Duopolies can exist in various forms, such as Cournot, Bertrand, or Stackelberg competition. These models demonstrate how firms in a duopoly can compete on output or price, depending on the assumptions made about firm behavior and market conditions.
Similar features are discernible in national political systems of party duopoly.
Duopoly models in economics and game theory
Cournot duopoly
Cournot model in game theory
In 1838,
Antoine Augustin Cournot published a book titled "Researches Into the Mathematical Principles of the Theory of Wealth" in which he introduced and developed this model for the first time. As an imperfect competition model, Cournot duopoly (also known as Cournot competition), in which two firms with identical cost functions compete with homogenous products in a static context, is also known as
Cournot competition. The Cournot model, shows that two firms assume each other's output and treat this as a fixed amount, and produce in their own firm according to this. The Cournot duopoly model relies on the following assumptions:
* Each firm chooses a quantity to produce independently
* All firms make this choice simultaneously
* The cost structures of the firms are public information
In this model, two companies, each of which chooses its own quantity of output, compete against each other while facing constant marginal and average costs. The market price is determined by the sum of the output of two companies.
is the equation for the market demand function.
* Market with two firms with constant marginal cost
* Inverse market demand for a homogeneous good:
* Where is the sum of both firms' production levels:
* Firms choose their quantity simultaneously (static game)
* Firms maximize their profit:
The general process for obtaining a Nash equilibrium of a game using the
best response functions is followed in order to discover a Nash equilibrium of Cournot's model for a specific cost function and demand function. A Nash Equilibrium of the Cournot model is a such that
For a given
solves: