Bertrand Paradox I
Week 6
Bertrand Paradox I Theoretical Model
Bertrand Model 2 companies
2 ice cream sellers on a beach
Price competition
Sellers set prices
Identical products
Same ice cream
Game played once
Price setting once
Market transparency
All consumers know both prices
Infinite price elasticity
Seller with lower price gets all customers
No capacity constraints Each seller can produce endless amounts of ice cream
Fixed Prices
Seller A
Each seller can set Low price High price
Seller B
High
Low
High
50% / 50%
0% / 100%
Low
100% / 0%
50% / 50%
Share of consumers
Continuous Prices Each seller can set any price Unique Nash Equilibrium
Prices equal costs (no fixed costs) Profits equal zero
In reality firms do make profits.
Competitive Strategy Tobias Kretschmer Professor of Management, LMU Munich
© 2013 LMU Munich
Week 6
Bertrand Paradox II Adjusting Model Assumptions
Bertrand Model 2 companies Price competition Identical products Game played once Market transparency Infinite price elasticity No capacity constraints
Model Assumptions (I/III) Identical products In reality, consumers have different taste and products are differentiated
Monopolization not possible
Each seller produces a different flavour of ice cream
Game played once
In reality, game has indefinite repetitions Collusion possible through threat of retaliation
Every summer season, sellers set their prices
Model Assumptions (II/III) Market transparency In reality, imperfect market transparency
Undercutting prices has an effect on some consumers only
Some consumers know price of one seller only
Infinite price elasticity
In reality, costs for consumers associated with switching seller Undercutting prices has limited effect
Sellers introduce loyalty programme (e.g. 10th ice cream for free)
Model Assumptions (II/III) No capacity constraints In reality, companies have limited capacity
No incentive to induce a price war over the complete demand
Each seller can produce limited amount of ice cream only
What Firms Can Do Firms can actively influence these aspects to avoid the Bertrand trap Agree on prices, implicitly or explicitly Play the game repeatedly, make sure there is no endpoint Limit your capacity Increase switching costs
Differentiate your product
Competitive Strategy Tobias Kretschmer Professor of Management, LMU Munich
© 2013 LMU Munich
Bertrand Paradox I Theoretical Model
Bertrand Model 2 companies
2 ice cream sellers on a beach
Price competition
Sellers set prices
Identical products
Same ice cream
Game played once
Price setting once
Market transparency
All consumers know both prices
Infinite price elasticity
Seller with lower price gets all customers
No capacity constraints Each seller can produce endless amounts of ice cream
Fixed Prices
Seller A
Each seller can set Low price High price
Seller B
High
Low
High
50% / 50%
0% / 100%
Low
100% / 0%
50% / 50%
Share of consumers
Continuous Prices Each seller can set any price Unique Nash Equilibrium
Prices equal costs (no fixed costs) Profits equal zero
In reality firms do make profits.
Competitive Strategy Tobias Kretschmer Professor of Management, LMU Munich
© 2013 LMU Munich
Week 6
Bertrand Paradox II Adjusting Model Assumptions
Bertrand Model 2 companies Price competition Identical products Game played once Market transparency Infinite price elasticity No capacity constraints
Model Assumptions (I/III) Identical products In reality, consumers have different taste and products are differentiated
Monopolization not possible
Each seller produces a different flavour of ice cream
Game played once
In reality, game has indefinite repetitions Collusion possible through threat of retaliation
Every summer season, sellers set their prices
Model Assumptions (II/III) Market transparency In reality, imperfect market transparency
Undercutting prices has an effect on some consumers only
Some consumers know price of one seller only
Infinite price elasticity
In reality, costs for consumers associated with switching seller Undercutting prices has limited effect
Sellers introduce loyalty programme (e.g. 10th ice cream for free)
Model Assumptions (II/III) No capacity constraints In reality, companies have limited capacity
No incentive to induce a price war over the complete demand
Each seller can produce limited amount of ice cream only
What Firms Can Do Firms can actively influence these aspects to avoid the Bertrand trap Agree on prices, implicitly or explicitly Play the game repeatedly, make sure there is no endpoint Limit your capacity Increase switching costs
Differentiate your product
Competitive Strategy Tobias Kretschmer Professor of Management, LMU Munich
© 2013 LMU Munich
