Refer to the normal-form game of price competition in the payoff matrix below. $\begin{array}{c}
\text { Firm B }\
\text { Firm A}
\begin{array}{|l|l|l|}
\hline & \text { Low Price } & \text { High Price } \
\hline & & \
\text { Low Price } & 0,0 & 50,-10 \
\hline & & \
\text { High Price } & -10,50 & 20,20\
\hline
\end{array}\end{array}$ Suppose the game is infinitely repeated,and the interest rate is 10 percent.Both firms agree to charge a high price,provided no player has charged a low price in the past.If both firms stick to this agreement,then the present value of firm A's payoffs are:
A) 220.
B) 110.
C) 330.
D) 550.

Question

Refer to the normal-form game of price competition in the payoff matrix below. $\begin{array}{c}
\text { Firm B }\
\text { Firm A}
\begin{array}{|l|l|l|} 
\hline & \text { Low Price } & \text { High Price } \
\hline & & \
\text { Low Price } & 0,0 & 50,-10 \
\hline & & \
\text { High Price } & -10,50 & 20,20\
\hline
\end{array}\end{array}$ Suppose the game is infinitely repeated,and the interest rate is 10 percent.Both firms agree to charge a high price,provided no player has charged a low price in the past.If both firms stick to this agreement,then the present value of firm A's payoffs are:
A) 220.
B) 110.
C) 330.
D) 550.

Quizplus · Accepted Answer

The present value of firm A's payoffs, if both firms stick to the agreement to charge a high price, can be calculated using the formula for the present value of a perpetuity: $PV = \frac{C}{r}$, where $C$ is the cash flow per period (in this case, the payoff of 20 for charging a high price) and $r$ is the interest rate (in this case, 10% or 0.1). Thus, $PV = \frac{20}{0.1} = 200$. However, since the question asks for the present value including the initial period, we add the payoff for the first period directly to this value, resulting in a total of $200 + 20 = 220$.

Refer to the Normal-Form Game of Price Competition in the Payoff