The King of Price

Calculator for Cournot Duopoly

This calculator grants you all solutions concepts discussed in this website under our previous assumptions.

Cournot Duopoly

> Consider two companies producing homogenous products competing with each other.

Price Function and Marginal Cost

> Price function must be in the form $p(q)=D-kq$ for some $D, q \in \mathbb{R}^+$.
> The marginal cost must be a positive constant $c \in \mathbb{R}^+$.
> Please click "Cournot Duopoly Payoff Matrix" before "Extortionate Zero-determinant Strategy" to update the game matrix.

Marginal cost:

Price Function:

Invalid input under general assumption of Cournot Competition

Non-cooperative Duopoly

Output level constituting Nash equilibrium is ( , ), with profit vector ( , )

Cooperative Duopoly

If cooperation allowed, joint profit is maximized at output level
Assuming both players share an equal amount of workload, profit for players is (, )

Without integral quantity assumption and conservative convention,

Firm 1 \ Firm 2	Cooperate (Produce )	Betray (Produce )
Cooperate (Produce )	()	()
Betray (Produce )	()	(0)

With integral quantity assumption and conservative convention,

Firm 1 \ Firm 2	Cooperate (Produce )	Betray (Produce )
Cooperate (Produce )	()	()
Betray (Produce )	()	()

Prototype Formula

Extortionate Payoff

$$s_x=\dfrac{P(T-R)+\chi\left[R(T-S)-P(T-R)\right]}{(T-R)+\chi(R-S)}$$

Extorted Payoff

$$s_y=\dfrac{\chi P(R-S)+\left[R(T-P)-S(R-P)\right]}{(T-R)+\chi(R-S)}$$

Extortionate Setup

Extortionate Factor

If the other player decides to accept the extortion, then:

Extortionate Payoff:

Extorted Payoff:

Limiting Behavior

When $\chi\to\infty$, $s_x =$ , $s_y = $ .

Under this value and above assumption, the game cannot be modelled as a Prisoner's Dilemma and the Zero-Determinant Strategy cannot be applied.