WEEK 3 - Oligopoly Markets Flashcards
What do markets differ according to?
- No of firms in market
- Ease of entry/exit
- Ability to differentiate
What are the most distinguishable elements of Oligopolies?
- Limited no of firms
- Limited Mkt power - Collectively shared
- Firms cannot ignore rival behaviour
What are the 3 model of Oligopolies?
- Cournot: Firms decide quantity (compete on Quantity), and price adjust to consumer demand
ONE SHOT GAME - SIMULTANEOUS DECISION - Bertrand: Firms set price (compete on price) and sell whatever demanded at those prices (most services)
SIMULTANEOUS - Stackelberg: 1st mover advantage -> Timing matters
Sequential Decision
What are the assumptions of a Duopoly?
- Two firms and none enter the market
- The firms have identical costs
- Firms sell identical products
- Firms set quantities simultaneously
E.g. Airline Market
What is Game Theory?
Set of tools to analyse strategic decision making
What is a game?
Interaction between players where they use strategies
What is a payoff?
Player’s valuation of the outcome of the game
What is an Action?
Move player makes at a specified stage of a game
What is a strategy?
Battle Plan specifying the action that a player will make based on info available at each move and for any possible contingency
When does Strategic Interdependence occur?
When player’s optimal strat depends on action of others
What are the assumptions of Game Theory?
All players are/have:
- Interested in maximising payoff (Profit, Utility, whatever)
- Have common knowledge of rules of game
- Each payoff depends on all actions taken by all players (duopoly interaction)
- Complete info (Pay off function, common knowledge betwen players) dif from perfect knowledge (player knows full history of game)
What is a static game?
- Each player acts simultaneously, only once
- Complete info about pay off function
- Imperfect info about rival moves
EXAMPLE OF A GAME AS WELL AS FINDING DOMINANT STRAT AND NASH EQUILIBRIUM
SEE IN NOTES
What is a Dominant Strategy?
An option regardless of rival choice
What is a best response?
A strategy that maxes player’s payoff given beliefs of rival strategies
What is a Nash Equilibrium?
Player has no incentive to change their action
What is the Linear Cournot Model?
- Homogenous product market with N firms
- Firm i sets quantity qi
- Total output: q = q1 + q2 + … + qn
- Market price given by p(q) = a - bq
- Linear Cost functions : Ci (qi) = ci qi - q - qi
Notation: q -i
What is the strat form of Cournot duopoly game?
Player: Firm 1 and 2
- Strat sets: Feasible output 0< or equal q1 < Q max
and 0 < equal to q2 < Q Max
with i = 1,2
What is the general calculation for residual demand?
p (qi, q-1) = (a - bq - i) - bqi = di (q-i)
SEE GRAPH IN NOTES
What is the residual demand given Q2
SEE GRAPH IN NOTES
What is the best reply if Q1 falls as Q2 rises
SEE GRAPH IN NOTES
What is the special case when Q2 = 0
SEE GRAPH IN NOTES
What is the calculation for general demand?
p = p (a) = p (q1 + q2 + q3…)
What is the calculation for linear demand?
p = a -bQ with Q = q1 + q2 + q3 ….
How do you calculate Linear Costs?
TCi = CiQi + Fi
- MC = MCi = Ci
AC = ACi = Ci + (Fi/Qi)
If identical firms: C1 = C2 = C3 = … = Ci Fi = F
How do you calculate the best replies response in a Duopoly?
SEE IN NOTES
WAYYYY TOO LONG TO DO AS FLASHCARD
What is the graph for a Cournot equilibrium?
If q1 produced too large than q2 produce at perf comp level and vice versa
- So, continue to move til Nash Equilibrium
(SEE IN NOTES)
What is a Bertrand Equilibrium/ Nash-Bertrand Equilibrium?
A set of prices such that no firm can obtain higher profits by choosing dif price if the other firms continue to charge these prices
What makes up the Bertrand Model?
- Homogenous Product - 2 Firms
- Identical MC’s
- Set price simultaneously to maximise profits
- No capacity constraints
What is the main strategic incentive in the Bertrand Model?
To undercut rival’s price
As a result of the undercutting that goes on in the Bertrand model what do Consumers typically do?
- Firms with lower prices attract all demand Q = P
- At equal prices, markets splits at a1 and a2 = 1- a1
- If P differs, all consumers buy only from the low price firms (p1 < p2 -> q1 = Q(p1), π1 = (p1 - c) Q (p1)
q2 = 0 , π2 = 0
Where capital Q is the market quantity
q is individual quantity
What happens with consumers if price is equal in the duopoly in the Bertrand model?
If P is equal consumers typically indifferent to buy from any of the 2 firms: Assume they equally share industry demand:
- P1 = P2 = P -> q1 = q2 = 1/2 Q(p) π1 π2 = 1/2 (p-c) Q (p)
When is undercutting optimal for a rival firm?
If one firm sets price at P>C, then undercutting optimal
i.e. if P2 = P>C then p1 = P -> π1 = 1/2(p-c)Q (p)
P1 = P - ε -> π1 = (P - ε - C) Q(P-ε)
SEE GRAPH IN NOTES
What is the best response for two firms under a Bertrand oligopoly?
For firm 1:
BRF 1. - If P2>PM (Monopoly Price)
-> P1 = PM
BRF 2. - If C P1 = P2 - ε
BRF 3. - If P2 < MC
-> P1 =MC
Symmetric for firm 2
What is a unique Nash equilibrium in Bertrand’s model?
Both firms set price = MC
What is the Bertrand Paradox?
By adding only one firm, we go from: the extreme of monopoly to the other extreme of perfect competition. Seems extreme.
- No mkt power
- Firms set P = MC -> Under Duopoly but same results as Perf Comp
What is the basic understanding for Stackelberg’s model?
- Dynamic games -> Sequential Decisions
- > Possibility for some firms to act before competitors, who can thus observe past choices
- > Leaders and Followers in the model
- Depend on nature of strat variables and on no of firms moving at dif stages
-> 1st mover must have some kind of commitment
What is Stackeberg’s model?
- 1 leader and 1 follower
1st move advantage
-> Firm get payoff increase in game where it is a leader rather than follower - Otherwise 2nd mover advantage
- Stackleberg leader knows follower will use BRF and so leader views residual demand as its demand
What is Quantity Competition in Stackelberg’s model?
- Similar to Cournot
- But one firm chooses quantity before the other
- Looking for sub game perfect equilibrium
What is the setting in Stackelberg’s model?
P (q1,q2) = a - q1 - q2 ; C1 = C2 = 0
Firm 1 = (leader) (Firm 2: Follower)
What is a Subgame perfect Nash equilibrium?
Is an equilibrium such that player’s strategies constitute Nash equilibrium in every subgame of original gam
- General Linear Inverse Demand: p = a-bQ
How can a Subgame perfect Nash equilibrium be found?
Via backward induction
- Determine optimal strategy of player who makes it last move in game
- Optimal action of the next to last moving player
Continues til all actions determined
- Eliminates all non credible threats
EXAMPLE OF SUBGAME NASH EQUILIBRIUM
SEE IN NOTES
What is the maths of Stackleberg?
SEE IN NOTES
