Harold has visited a casino and paid an entry fee of $20,000 to play the game of cards. Below is the payoff table in terms of the decision to play or not to play the game (Note: Harold will not pay the entry fee if he does not want to play and the below payoff table includes the entry fee).

$$\begin{array} { | l | c | c | }
\hline { \text { Decision } } & &{ \text { State of Nature } } \
\hline & \text { Win } ( \$ ) & \text { Lose } ( \$ ) \
\hline \text { Play the game, } d _ { 1 } & 50,000 & - 20,000 \
\hline \text { Do not play the game, } d _ { 2 } & 0 & 0 \
\hline
\end{array}$$
a. In his previous visits, Harold has won 1 out of every 5 games that he has played. Use the expected value approach to recommend a decision.
b. Assume that the utilities for 50,000 and -20,000 are 10 and 0, respectively. If a particular decision maker assigns an indifference probability of 0.0001 to the $0 payoff, would Harold play the game? Use expected utility to justify your answer.

Question

Harold has visited a casino and paid an entry fee of $20,000 to play the game of cards. Below is the payoff table in terms of the decision to play or not to play the game (Note: Harold will not pay the entry fee if he does not want to play and the below payoff table includes the entry fee).
​
​ $$\begin{array} { | l | c | c | } 
\hline  { \text { Decision } } & &{ \text { State of Nature } } \
\hline  & \text { Win } ( \$ ) & \text { Lose } ( \$ ) \
\hline \text { Play the game, } d _ { 1 } & 50,000 & - 20,000 \
\hline \text { Do not play the game, } d _ { 2 } & 0 & 0 \
\hline
\end{array}$$ ​ 
a. In his previous visits, Harold has won 1 out of every 5 games that he has played. Use the expected value approach to recommend a decision.
b. Assume that the utilities for 50,000 and -20,000 are 10 and 0, respectively. If a particular decision maker assigns an indifference probability of 0.0001 to the $0 payoff, would Harold play the game? Use expected utility to justify your answer.

Quizplus · Accepted Answer

The Answer of Harold has visited a casino and paid an entry fee of $20,000 to play the game of cards. Below is the payoff table in terms of the decision to play or not to play the game (Note: Harold will not pay the entry fee if he does not want to play and the below payoff table includes the entry fee).
​
​ $$\begin{array} { | l | c | c | } 
\hline  { \text { Decision } } & &{ \text { State of Nature } } \
\hline  & \text { Win } ( \$ ) & \text { Lose } ( \$ ) \
\hline \text { Play the game, } d _ { 1 } & 50,000 & - 20,000 \
\hline \text { Do not play the game, } d _ { 2 } & 0 & 0 \
\hline
\end{array}$$ ​ 
a. In his previous visits, Harold has won 1 out of every 5 games that he has played. Use the expected value approach to recommend a decision.
b. Assume that the utilities for 50,000 and -20,000 are 10 and 0, respectively. If a particular decision maker assigns an indifference probability of 0.0001 to the $0 payoff, would Harold play the game? Use expected utility to justify your answer.

Harold Has Visited a Casino and Paid an Entry Fee