Question

Two companies, Chevron and Shell, are the only two gas stations operating in a small town. Each company must simultaneously display their prices, choosing between a high price and low price. The profits each firm can potentially earn are displayed in the payoff matrix displayed below:

Chevron Decisions High Price Low Price S: $5,000 C: $5,500 S: $1,000 C: $8,000 High Price Shell Decisions S: $7,500 C: $1,500 S: $3,000 Low Price C: $2,800

a. What is Chevron’s most likely decision (what is their dominant strategy)?

b. What is Shell’s most likely decision (what is their dominant strategy)?

c. What is the most expected outcome (what is the Nash equilibrium)? How much will each firm profit?

d. Explain why displaying prices every day, so this is not a one-time game as this matrix would suggests, alters the perceived payoff in a way that changes the Nash equilibrium? In other words, why would doing this multiple times lead to a different outcome than doing it once?

Answer 1

Shell/ chevron	high	low
High	(5000, 5500)	(1000,8000•)
Low	(7500*,1500)	(3000*,2800•)

A) chevron has dominant strategy = charge low price .

Chevron always earns higher profit by playing low as against high , for any given strategy of shell , thus low is a dominant strategy for chevron

B) shell's most likely decision or dominant strategy is low because for any given strategy of chevron, shell always earns higher profit when it plays low

C) NE: < low, low>

Shell earns 3000 & chevron earns 2800

D) if both firms interact repeatedly that is, if the one stage game is played for a large number of times, then both firms could benefit by cooperating .

Hence rather than charging low prices as in Nash equilibrium of one stage game , if both firms could charge higher price than both will benefit , since the equilibrium payoff from Cooperation for both forms will be higher than their Nash equilibrium payoffs.

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