Consider Bob's decision problem: Sunny Cloudy Rainy Beach 2 3 4 Park 3 4 4 Mall 2 4 2 Which of the following statements is TRUE? Beach is a strongly dominated choice for Bob Park is a strongly dominated choice for Bob Mall is a strongly dominated choice for Bob Bob has no strongly dominated choices
Question
Consider Bob's decision problem:
Sunny Cloudy Rainy
Beach 2 3 4 Park 3 4 4 Mall 2 4 2
Which of the following statements is TRUE?
Beach is a strongly dominated choice for Bob
Park is a strongly dominated choice for Bob
Mall is a strongly dominated choice for Bob
Bob has no strongly dominated choices
Solution
To determine if a choice is strongly dominated, we need to compare each choice's outcomes under all possible states of the world (in this case, weather conditions) to the outcomes of the other choices.
A choice is strongly dominated if there is another choice that always yields a better outcome, no matter what the state of the world is.
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Beach vs Park: In all weather conditions (Sunny, Cloudy, Rainy), Park either yields a better outcome or the same outcome (3>=2, 4>=3, 4>=4). So, Beach is strongly dominated by Park.
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Beach vs Mall: In some weather conditions (Sunny, Rainy), Beach yields a better outcome than Mall (2>2, 4>2). So, Beach is not strongly dominated by Mall.
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Park vs Mall: In some weather conditions (Sunny, Rainy), Park yields a better outcome than Mall (3>2, 4>2). In other conditions (Cloudy), Mall yields a better outcome than Park (4>3). So, Park is not strongly dominated by Mall.
Therefore, the statement "Beach is a strongly dominated choice for Bob" is TRUE. The other statements are FALSE.
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