Consider the Following Problem with Four States of Nature,three Decision

Essay

Consider the following problem with four states of nature,three decision alternatives,and the following payoff table (in $'s): $$\begin{array} { l | c c c c } & s _ { 1 } & s _ { 2 } & s _ { 3 } & s _ { 4 } \\\hline d _ { 1 } & 200 & 2600 & - 1400 & 200 \\d _ { 2 } & 0 & 200 & - 200 & 200 \\d _ { 3 } & - 200 & 400 & 0 & 200\end{array}$$ The indifference probabilities for three individuals are: $$\begin{array} { r c c c } \text { Payoff } & \text { Person 1 } & \text { Person 2 } & \text { Person 3 } \\\hline\$ 2600 & 1.00 & 1.00 & 1.00 \\\$ 400 & .40 & .45 & .55 \\\$ 200 & .35 & .40 & .50 \\\$ 0 & .30 & .35 & .45 \\- \$ 200 & .25 & .30 & .40 \\- \$ 1400 & 0 & 0 & 0\end{array}$$
a. Classify each person as a risk avoider, risk taker, or risk neutral.
b. For the payoff of $400, what is the premium the risk avoider will pay to avoid risk? What is the premium the risk taker will pay to have the opportunity of the high payoff?
c. Suppose each state is equally likely. What are the optimal decisions for each of these three people?