HW Review

1. HW Review Suppose a game has a payoff matrix of: Calculate the expected values for the following strategy:

2. 9.2 Mixed Strategies The Acme Chemical Corporation has two plants. A single inspector is assigned to check that the plants do not dump waste into the river. • If he discovers plant A dumping waste, Acme is fined $20,000. • If he discovers plant B dumping waste, Acme is fined $50,000. Suppose the inspector visits one of the pants each day and he chooses, on a random basis to visit plant B 60% of the time. Acme schedules dumping from its two plants on a random basis, one plant per day, with plant B dumping waste on 70% of the days. How much is Acme’s average fine per day? • Write a payoff matrix • Write the mixed strategies. • Find the expected value.

3. 9.2 Mixed Strategies A small business owner must decide whether to carry flood insurance. She may insure her business for: • $2 million for $100,000 • $1 million for $50,000 or • $.5 million for $30,000. Her business is worth $2 million. There is a flood serious enough to destroy her business an average of every 10 years. In order to save insurance premiums, she decides each year on a probabilistic basis how much insurance to carry.She chooses: • $2 million 20% of the time • $1 million 20% of the time • $.5 million 20% of the time • No insurance 40% of the time What is her average annual loss? • Write a payoff matrix in terms of millions • Write the mixed strategies. • Find the expected value.

4. 9.2 Mixed Strategies • Problems to complete from section 9.2 • Pg. 452 #3, 4