Bertrand competition with
homogeneous products
• n firms
• Constant marginal costs c i >0
• Each firm set price pi simultaneously and
independently
• Linear demand Q=A-Bp where
p=min[p1,.., pn]
• Consumers buy only from firms with the
lowest prices
Equilibrium
The Nash equilibria of this game are as follows:
• If there is a unique firm with the lowest marginal
costs, she and at least one firm charge the
second lowest marginal costs. All others charge
at least this price. All sales are to the firm with
the lowest marginal costs.
• If there are several firms with the lowest
marginal costs, they all charge this costs and
share the market. All other firms charge at least
this price.
Results from experiment
• First 7 rounds: fixed partners, duopoly
• Next 10 rounds: random matching, tripoly
• Last 10 rounds: random matching,
duopoly, firms sold perfect complements
• 18 / 7 / 12/ 16 subjects
Vertical Monopoly
• Solved in Stackelberg-style:
• First the reaction function of the retailer
(who moves second) is determined.
• This is used to determine the profit
function of the wholesaler and to find his
profit-optimum
• “backward induction”, subgame perfect
equilibrium
• Result: worse than monopoly
Free entry (and exit)
• With free entry firms will enter until all profits are
eroded.
• Example: Cournot oligopoly,
– Prni=(A-c)2/B(n+1)2
– Entry costs F
– In equilibrium entry will occur until F= Prni , ignoring
the integer problem
– There will be n=(A-c)/Sqrt(BF) firms in the market
• Example: monopolistic competition
• Example: contestable markets