Dr. Fine and Dr. Feelgood are the only two medical doctors offering immediate walk-in medical services in the town of Springfield. That is, they operate in a duopoly. Each doctor can charge either a high price or a low price for a standard medical visit. The accompanying matrix shows their payoffs, in profits per patient (in dollars), for any choice that the two doctors can make.

1. Suppose the two doctors play a one-shot game-that is, they interact only once and never again. What will be the Nash (non-cooperative) equilibrium in this one-shot game?

2. Now suppose the two doctors play this game twice. Also, suppose each doctor can play one of two strategies: it can play either "always charge the low price" or "tit for tat"- that is, it starts off charging the high price in the first period, and then in the second period it does whatever the other doctor did in the previous period. Write down the payoffs to Dr. Fine from the following four possibilities:

a) Dr. Fine plays "always charge the low price" when Dr. Feelgood also plays "always charge the low price."

FIRST Period Payoffs SECOND Period Payoffs TOTAL Payoffs
Charges
(high or low) Charges
(high or low)
Fine Fine
Feelgood Feelgood

b) Dr. Fine plays "always charge the low price" when Dr. Feelgood plays "tit for tat."

FIRST Period Payoffs SECOND Period Payoffs TOTAL Payoffs
Charges
(high or low) Charges
(high or low)
Fine Fine
Feelgood Feelgood

c) Dr. Fine plays "tit for tat" when Dr. Feelgood plays "always charge the low price."

FIRST Period Payoffs SECOND Period Payoffs TOTAL Payoffs
Charges
(high or low) Charges
(high or low)
Fine Fine
Feelgood Feelgood

d) Dr. Fine plays "tit for tat" when Dr. Feelgood also plays "tit for tat."

FIRST Period Payoffs SECOND Period Payoffs TOTAL Payoffs
Charges
(high or low) Charges
(high or low)
Fine Fine
Feelgood Feelgood