The U.S. government has decided to build a new off ramp for Interstate 5 in California. Exxon and Shell are both interested in building a gas station near the new off ramp. They can build the gas station near the off ramp for northbound traffic or they could build the gas station near the off ramp for southbound traffic. The profits for each outcome are illustrated in the accompanying payoff table: Shell Shell northbound southbound Exxon receives Exxon receives $60,000 profit $110,000 profit Exxon northbound Shell receives Shell receives $50,000 profit $100,000 profit Exxon receives Exxon receives $80,000 profit $50,000 profit Еxxon southbound Shell receives Shell receives $120,000 profit $50,000 profit
The U.S. government has decided to build a new off ramp for Interstate 5 in California. Exxon and Shell are both interested in building a gas station near the new off ramp. They can build the gas station near the off ramp for northbound traffic or they could build the gas station near the off ramp for southbound traffic. The profits for each outcome are illustrated in the accompanying payoff table: Shell Shell northbound southbound Exxon receives Exxon receives $60,000 profit $110,000 profit Exxon northbound Shell receives Shell receives $50,000 profit $100,000 profit Exxon receives Exxon receives $80,000 profit $50,000 profit Еxxon southbound Shell receives Shell receives $120,000 profit $50,000 profit
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.9P
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![The U.S. government has decided to build a new off ramp for Interstate 5 in California. Exxon and Shell are both interested
in building a gas station near the new off ramp. They can build the gas station near the off ramp for northbound traffic or
they could build the gas station near the off ramp for southbound traffic. The profits for each outcome are illustrated in the
accompanying payoff table:
Shell
Shell
northbound
southbound
Exxon receives
Exxon receives
$60,000 profit
$110,000 profit
Exxon northbound
Shell receives
Shell receives
$50,000 profit
$100,000 profit
Exxon receives
Exxon receives
$80,000 profit
$50,000 profit
Exxon
southbound
Shell receives
Shell receives
$120,000 profit
$50,000 profit
a. Select the Nash equilibrium, or equilibria, that occur if Exxon and Shell make these decisions simultaneously.
Exxon builds southbound and Shell builds southbound.
Exxon builds northbound and Shell builds southbound.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0bd246c0-da09-4f0b-8490-d87ea5e25619%2F6a769f8c-94c4-4d91-946b-67943ea11f46%2F4fyubsm_processed.png&w=3840&q=75)
Transcribed Image Text:The U.S. government has decided to build a new off ramp for Interstate 5 in California. Exxon and Shell are both interested
in building a gas station near the new off ramp. They can build the gas station near the off ramp for northbound traffic or
they could build the gas station near the off ramp for southbound traffic. The profits for each outcome are illustrated in the
accompanying payoff table:
Shell
Shell
northbound
southbound
Exxon receives
Exxon receives
$60,000 profit
$110,000 profit
Exxon northbound
Shell receives
Shell receives
$50,000 profit
$100,000 profit
Exxon receives
Exxon receives
$80,000 profit
$50,000 profit
Exxon
southbound
Shell receives
Shell receives
$120,000 profit
$50,000 profit
a. Select the Nash equilibrium, or equilibria, that occur if Exxon and Shell make these decisions simultaneously.
Exxon builds southbound and Shell builds southbound.
Exxon builds northbound and Shell builds southbound.
![a. Select the Nash equilibrium, or equilibria, that occur if Exxon and Shell make these decisions simultaneously.
Exxon builds southbound and Shell builds southbound.
Exxon builds northbound and Shell builds southbound.
Exxon builds southbound and Shell builds northbound.
Exxon builds northbound and Shell builds northbound.
b. Use the information in the payoff table to create a game tree for this sequential move game. This part is not graded, but
you will need to make the game tree on your own to answer the following questions.
c. The Nash equilibrium for the sequential move game where Exxon moves first is that Exxon builds
northbound
and Shell builds
northbound
southbound
southbound
Now suppose that
and builds a gas station before Exxon.
d. The Nash equilibrium for the sequential move game where Shell moves first is that Shell builds
and
northbound
Exxon builds
northbound
southbound](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0bd246c0-da09-4f0b-8490-d87ea5e25619%2F6a769f8c-94c4-4d91-946b-67943ea11f46%2Fjank904_processed.png&w=3840&q=75)
Transcribed Image Text:a. Select the Nash equilibrium, or equilibria, that occur if Exxon and Shell make these decisions simultaneously.
Exxon builds southbound and Shell builds southbound.
Exxon builds northbound and Shell builds southbound.
Exxon builds southbound and Shell builds northbound.
Exxon builds northbound and Shell builds northbound.
b. Use the information in the payoff table to create a game tree for this sequential move game. This part is not graded, but
you will need to make the game tree on your own to answer the following questions.
c. The Nash equilibrium for the sequential move game where Exxon moves first is that Exxon builds
northbound
and Shell builds
northbound
southbound
southbound
Now suppose that
and builds a gas station before Exxon.
d. The Nash equilibrium for the sequential move game where Shell moves first is that Shell builds
and
northbound
Exxon builds
northbound
southbound
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