Lecture 7 - Oligopoly Flashcards
The Bertrand duopoly model?
There are 2 identical firms, each with cost function C(qi)=mqi
Firms choose prices:
Firm 1 chooses p1
Firm 2 chooses p2
Market demand is D(p): given prices, the market determines total quantity
=Consumers buy from the firm with the lowest price
=If prices are the same (p1=p2) the two firms split the market equally
Where is the EQ (price) / NE in a Bertrand Duopoly Model?
No firm cans set pm, but all consumers buy from p=m
If both set p>m, both would have an incentive to decrease p a little bit to capture more demand. This leads continuous decreasing until p=m is reached for both. Which would then naturally mean that EQ for Bertand is at p1=p2=m, just like a Competitive Market! (p=MC)
Appropriate modelling choice: price or quantity?
for Monopoly and Oligopoly
Monopoly: it doesn’t matter
Oligopoly: price and quantity competitions lead to different residual demands. From the point of view of firm i:
Price competition
rival firm j willing to serve any demand at pj
i’s residual demand: market demand at pipj and perfectly elastic at pi = pj
=>So, residual demand is very sensitive to price changes
Quantity competition
rival firm j is willing to sell qj (irrespective of price obtained)
i’s residual demand: “what’s left” (i.e., market demand-qj)
=>So, residual demand is less sensitive to price changes
How do firms behave in the market place?
Stick to a price and sell any quantity at this price?
or
Stick to a quantity and sell this quantity at any price?
Stick to a price and sell any quantity at this price:
Price Competition: appropriate choice when:
- Unlimited capacity
- Prices more difficult to adjust in the SR than quantities
- Example: Pepsi vs. Coca Cola
Stick to a quantity and sell this quantity at any price:
Quantity Competition: appropriate choice when:
- Limited capacity (even if firms are price-setters)
- Quantities more difficult to adjust in the SR than prices
Example: Cournot: Stock market, OPEC (output by competitors can easily be decreased, but not increased)
Influence of technology! (e.g. Print-on-demand vs. batch printing)
What are the assumptions of Bertrand Price Competition Modelling?
- Homogenous products
- Consumer only buy from lowest priced firm (location and other determinants irrelevant)
- No capacity constraints
Why does a subgame perfect Nash equilibrium rule out non-credible threats?
The Subgame Perfect Nash Equilibrium (SPNE) is a refinement of the Nash equilibrium.
It requires that each player plays a best response to the other players’ actions in each subgame.
A non-credible threat is one that is not a best-response in the subgame where it could be played.
Why do firms in the pure Bertrand game have no market power?
The firms in the pure Bertrand model are identical and produce perfect substitutes.
Moreover, each firm can supply the whole market and consumers always buy from the cheapest firm.
In such a market, each firm has an incentive to price marginally lower than its competitor to supply the whole market instead of half of it. Both firms will undercut each other’s price until they reach marginal costs.
Is the prisoner’s dilemma a sequential game if one prisoner moves first and the other moves second? Explain your answer.
Yes, it is a sequential game, but players do not observe each other’s actions.
This is called a Sequential game with complete and imperfect information.
Information is complete because each player knows each players’ payoffs, and each player knows that each player knows each players’ payoff … etc. It is imperfect because the players do not observe each other’s actions.
