Question

2 Game Theory Suppose EatUp and HealthyF ̈ud both operate health-oriented fast-casual restaurants in Portland, Oregon. Firms make $15 on every grain bowl sold, and there are a million customers that wish to buy grain bowls this year. Currently, EatUp and HealthyF ̈ud split the market evenly. Consumers in Portland are very eco-conscious. Right now, both EatUp and HealthyF ̈ud generate significant plastic waste through disposable bowls and utensils used for to-go orders. A new law requires restaurants producing plastic waste to choose one of the below options: 1. Pay $500,000 for a plastic producer permit for the upcoming year 2. Pay $250,000 for a permit for the upcoming year and submit a proposal for a slow adoption of greener practices to start the following year 3. Invest $2,500,000 to immediately eliminate their plastic waste in the upcoming year and use greener materials going forward Consumers know if a company immediately adopts greener materials, but does not know if a company submits a plan for future adoption. If both companies immediately adopt green policies, they will split the market. If only one immediately adopts greener policies, that restaurant will get 60% of all customers. Otherwise, the restaurants split the market. EatUp HealthyF ̈ud Permit Permit & Plan Go Green Permit ( , ) ( , ) ( , ) Permit & Plan ( , ) ( , ) ( , ) Go Green ( , ) ( , ) ( , ) a. Say the law is enacted January 1, 2023, and the restaurants are deciding what to do at the end of 2022. Fill-in the above payoff matrix for 2023 based on the information provided. b. Define a Nash equilibrium, find the Nash equilibrium of this game. c. Define a dominated strategy and a dominant strategy, and identify all dominated and 2 dominant strategies in the game. d. What happens if the options available to restaurants are instead: 1. Pay $500,000 for a plastic producer permit for the upcoming year 2. Pay $700,000 for a permit for the upcoming year and submit a proposal for a slow adoption of greener practices to start the following year 3. Invest $1,500,000 to immediately eliminate their plastic waste in the upcoming year and use greener materials going forward Revise the payoff matrix based on the new information provided and find all of the new Nash equilibria.

2 Game Theory
Suppose EatUp and HealthyF ̈ud both operate health-oriented fast-casual restaurants in
Portland, Oregon. Firms make $15 on every grain bowl sold, and there are a million
customers that wish to buy grain bowls this year. Currently, EatUp and HealthyF ̈ud split
the market evenly.
Consumers in Portland are very eco-conscious. Right now, both EatUp and HealthyF ̈ud
generate significant plastic waste through disposable bowls and utensils used for to-go
orders. A new law requires restaurants producing plastic waste to choose one of the
below options:
1. Pay $500,000 for a plastic producer permit for the upcoming year
2. Pay $250,000 for a permit for the upcoming year and submit a proposal for a slow
adoption of greener practices to start the following year
3. Invest $2,500,000 to immediately eliminate their plastic waste in the upcoming year
and use greener materials going forward
Consumers know if a company immediately adopts greener materials, but does not know
if a company submits a plan for future adoption. If both companies immediately adopt
green policies, they will split the market. If only one immediately adopts greener policies,
that restaurant will get 60% of all customers. Otherwise, the restaurants split the market.
EatUp
HealthyF ̈ud
Permit Permit & Plan Go Green
Permit ( , ) ( , ) ( , )
Permit & Plan ( , ) ( , ) ( , )
Go Green ( , ) ( , ) ( , )
a. Say the law is enacted January 1, 2023, and the restaurants are deciding what to do
at the end of 2022. Fill-in the above payoff matrix for 2023 based on the information
provided.
b. Define a Nash equilibrium, find the Nash equilibrium of this game.
c. Define a dominated strategy and a dominant strategy, and identify all dominated and
2
dominant strategies in the game.
d. What happens if the options available to restaurants are instead:
1. Pay $500,000 for a plastic producer permit for the upcoming year
2. Pay $700,000 for a permit for the upcoming year and submit a proposal for a slow
adoption of greener practices to start the following year
3. Invest $1,500,000 to immediately eliminate their plastic waste in the upcoming year
and use greener materials going forward
Revise the payoff matrix based on the new information provided and find all of the new
Nash equilibria.

Added by Kimberly P.

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