1. HW Review Suppose a game has a payoff matrix of: Calculate the expected values for the following strategy: R WinsProb a)Prob b)Prob c)Prob d) R1, C111*.5=.5.3*.4=.120*.4=0.1*.2=.02 R1, C201*.4=.4.3*.4=.120*0=0.1*.2=.02 R1, C321*.1=.1.3*.2=.060*.6=0.1*.6=.06 R2, C10*.5=0.3*.4=.12.5*.4=.2.1*.2=.02 R2, C220*.4=0.3*.4=.12.5*0=0.1*.2=.02 R2, C300*.1=0.3*.2=.06.5*.6=.3.1*.6=.06 R3, C100*.5=0.4*.4=.16.5*.4=.2.8*.2=.16 R3, C20*.4=0.4*.4=.16.5*0=0.8*.2=.16 R3, C30*.1=0.4*.2=.08.5*.6=.3.8*.6=.48

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. OutcomeR WinsProbability Row 1, Col 1 Row 1, Col 2 Row 2, Col 1 Row 2, Col 2

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