A way of finding a competitive price of a product or a service. Reference: https://thismatter.com/economics/oligopoly-game-theory.htm

1. Game Theory of
Oligopolistic Pricing Strategies

2. Pricing Strategy
A way of finding a competitive price of a product or a service.
This strategy is combined with the other marketing pricing strategies that are the
4P strategy (products, price, place and promotion) economic patterns,
competition, market demand and finally product characteristic.

3. Oligopolistic Market
A market dominated by a few producers.
Like in monopolistic markets, in oligopolistic markets, the profit maximising strategy is to produce that
quantity of product where marginal revenue = marginal cost.
Interdependence problem: It is difficult for a firm in an oligopoly to determine its marginal revenue
because
the quantity of product that can be sold for a given price
will depend on
the prices charged by the other firms and the quantity that they produce.

4. Using Game Theory to Solve Interdependence Problem
We can use Game Theory to analyse strategies used by individual players that
take into account what the other players will do.
A common scenario for applying game theory to decision-making is the
prisoners' dilemma.

5. The Prisoners' Dilemma
Bennie and Stella were arrested for robbing banks. Each was interrogated in
separate rooms.
Role:
● if they both confessed, they would both get 5 years in prison;
● if one confessed, the confessor would go free while the other one would get
10 years;
● if neither confessed, then they would each get 2 years.

6. Payoff Matrix (Possibilities)

7. Payoff Matrix (Possibilities)
Stella
Bennie
Bennie
Silent
Silent
Silent
Confesses
Confesses
Confesses
5, 5
0, 10
2, 2
10, 0

8. Scenario
● The best possibility for both as a group would be if neither confessed, which
would mean that they would only have to spend 2 years in prison.
● The worst possibility for both of them as a group is if they both confessed —
then they would have to spend 5 years in prison.

9. Scenario
● As individuals, they may be able to do better or worse, depending on how
successfully they anticipate what the other will do:
○ If Stella confesses, the worst she can do is spend 5 years in prison (Bennie confesses), and
the best that she can do is go free (Bennie silent). Called dominant strategy which is the
strategy to take when it is impossible to anticipate their decision.
○ if Stella silent, then she will either spend 10 or 2 years in prison, depending on whether
Bennie confesses or not. Stella would probably only choose silence if she was fairly
confident that Bennie would not confess or silent. If not confident, Stella choose
dominat strategy.

10. Game Theory in Oligopolistic Market
● When firms in an oligopoly must decide about quantity and pricing, they must
consider what the other firms will do, since quantity and price are inversely
related.
● If all the firms produce too much, then the price may drop below their average
total costs, causing them losses. (Both “confesses”).
● If they can restrict quantity to that which corresponds to where marginal cost
= marginal revenue for the oligopoly as a whole, then they can maximize
their profits.

11. The Prisoner's Dilemma Scenario Advantage
● They usually know what the other firms did in the past, so they can decide on
quantity and pricing based on the assumption that they will act in the same
way in the future.
● If the firm is wrong in its anticipation, then they can make corrections in its
production schedule.
● Where firms have a history of working together, they can choose a dominant
strategy based on the choices that the other firms have made, which is called
a Nash equilibrium,

12. Cartel Strategy
● Sometimes, firms in an oligopoly try to eliminate guesswork by forming a
cartel, where they agree on a particular output, so that they can sell their
output at a profit-maximizing price.
● Cartels often fail because one or more firms will be tempted to cheat, since
this will allow them to earn outsized profits, especially if they are a smaller
firm that contributes only a small share of the total output of the oligopoly.
● For that would allow the firm to sell a greater quantity at the profit
maximizing price without lowering demand, and therefore, the price.

13. Detail
● When firms in a cartel cooperate by
restricting quantity for higher prices,
then each firm gets Po for its product by
restricting its quantity to the agreed
amount Qo (it is assumed that Qo is
equal to each firm's MR = MC output),
and each firm earns the revenue above
its marginal cost represented by the
areas 1 + 3 in the diagram on the left.
● Hence, the oligopoly earns what a
monopoly would earn.
● MR = Marginal Revenue
● MC = Marginal Cost
● D = Market Demand, Price

14. Detail
● When none of the cartel members
cooperate, then the quantity increases
to Qc and the market price declines to
the competitive price Pc, and each firm
in the oligopoly earns 3 + 4 above their
marginal cost.
● MR = Marginal Revenue
● MC = Marginal Cost
● D = Market Demand, Price

15. Detail
● If a firm cheats, then it earns: 1 + 2 + 3
+ 4 by producing more until MC = Po,
which is equal to the quantity, Qcheater.
● This assumes that the firm produces
only a small portion of the output of the
oligopoly.
● Otherwise, the firm's increased output
would cause the market price to
decline, and the market demand curve
for the oligopoly as a whole would shift
to the left.
● MR = Marginal Revenue
● MC = Marginal Cost
● D = Market Demand, Price

16. “The economists who use more mathematics are somehow
more respected than those who use less.”
John Forbes Nash, Jr.