DynamicPricing动态定价

PVCost of cheating
=
C1 (1 + r)N+1
+
C2 (1 + r)N+2
+
+
(1
CP + r)N
+P
Benefit to Intel for cheating
AMD’s price
High
Low
Intel’ s price
High Low
A: Cooperation
$5, $2.5
Cooperation defined
AMD’s price
High
Low
Intel’ s price
A: Cooperation
High $5, $2.5
B: AMD cheats
$2, $3
C: Intel cheats
Low
$6, $0.5
D: Noncooperation (Nash)
$3, $1
• What will happen if Intel decides to “cheat”?
• Punishment may deter Intel from cheating.
Punishment: A Credible Threat
AMD’s price
High
Low
Intel’ s price
$6, $0.5
$3, $1
Payoffs in millions of dollars of profit per week.
Dominant Strategy for Intel
AMD’s price
High
Low
Intel’ s price
High Low
A: Cooperation
B: AMD cheats
N = 2 and r = 0.001
Present value of benefits of cheating for 2 weeks with discount rate of 5.2 annual percentage rate:
$1, 000,000 $1, 000,000 PVBenefit = (1 + 0.001)1 + (1 + 0.001)2
$2,000,000 $2, 000, 000 PVCosts = (1 + 0.001)3 + (1 + 0.001)4
= $1, 994, 012 + $1, 992, 020 = $3, 986, 032
Intel decides to cooperate
PVCosts = $3, 986, 032 > $1, 997, 003 = PVBenefits
• Now suppose Intel and AMD post prices every Monday at 8:00 a.m.
• Also suppose that they have BOTH been setting high prices for the past several months.
$5, $2.5
$2, $3
C: Intel cheats
D: Noncooperation (Nash)
$6, $0.5
$3, $1
Payoffs in millions of dollars of profit per week.
Dynamic or Repeated Pricing Decisions
$5, $2.5
$2, $3
C: Intel cheats
D: Noncooperation (Nash)
$6, $0.5
$3, $1
Payoffs in millions of dollars of profit per week.
Low is dominant strategy
AMD’s price
Deciding to Cooperate (cont’d)
Present value of benefits of cheating for N time periods:
PVBenefit of cheating
=
B1 (1 + r)1
+
B2 (1 + r)2
+
+
(1
BN + r)N
Present value of costs of cheating for P time periods:
• Decision to cooperate is same as deciding not to cheat (i.e., refrain from cheating)
• Principle: Cooperation maximizes value of firm when PV of costs of cheating exceed PV of the benefits from cheating. Cooperation results only when all firms decide to cooperate (refrain from cheating).
High
Low
Intel’ s price
High Low
A: Cooperation
$5, $2.5
B: AMD cheats
$2, $3
C: Intel cheats
$6, $0.5
D: Noncooperation (Nash)
$3, $1
Payoffs in millions of dollars of profit per week.
= $999,000 + $998, 003 = $1, 997, 003
P = 2 and r = 0.001
Present value of costs of cheating for 2 weeks with discount rate of 5.2 annual percentage rate:
Payoffs in millions of dollars of profit per week.
Noncooperation in the onetime decision
AMD’s price
High
Low
Intel’ s price
High Low
A: Cooperation
B: AMD cheats
Tutorial: Dynamic Pricing: Repeated Pricing Decisions
Dynamic Pricing
• Cournot and Bertrand duopoly involved onetime decisions
• Most business decisions concerning P or Q are made repeatedly over time
B: AMD cheats
$2, $3
C: Intel cheats
$6, $0.5
D: Noncooperation (Nash)
$3, $1
Payoffs in millions of dollars of profit per week.
Cost to Intel for cheating
AMD’s price
High
Low
Intel’ s price
High Low
A: Cooperation
B: AMD cheats
$5, $2.5
$2, $3
C: Intel cheats
D: Noncooperation (NБайду номын сангаасsh)
$6, $0.5
$3, $1
Payoffs in millions of dollars of profit per week.
Deciding to Cooperate
• Managers should make decisions that maximize value of firm.
• Value of firm = sum of discounted expected profits in current and future periods
Intel and AMD: one-time pricing decision
AMD’s price
High
Low
Intel’ s price
High Low
A: Cooperation
B: AMD cheats
$5, $2.5
$2, $3
C: Intel cheats
D: Noncooperation (Nash)
• Both firms worse off than if they could have somehow cooperated in making their decisions
• Let’s review this situation before we examine how repeated decision making changes things
• “Dynamic” pricing means multiperiod or repeated pricing decisions
• Dynamic or repeated pricing can result in cooperative pricing by rivals and higher profits
High Low
A: Cooperation
B: AMD cheats
$5, $2.5
$2, $3
C: Intel cheats
D: Noncooperation (Nash)
$6, $0.5
$3, $1
Payoffs in millions of dollars of profit per week.
Review One-Period Pricing
• Recall outcome of one-time Prisoner’s Dilemma
• Firms pursuing their own individual best interests end up in noncooperative Nash equilibrium cell