Question: Soapy Inc. and Suddies Inc. are the only producers of soap powder. They collude and agree to share the market equally. If neither firm cheats on the agreement, each makes $1 million profit. If either firm cheats, the cheat makes a profit of $1.5 million, while the complier incurs a loss of $0.5 million. If both cheat, they break even. Neither firm can monitor the other's actions.
a) What are the strategies in this game? Construct the payoff matrix for this game.
b) What is the equilibrium of this game if it is played only once? Is the equilibrium a dominant-strategy equilibrium? Explain.
c) If Soapy Inc. and Suddies Inc. repeatedly play the duopoly game. What are the strategies that each firm might adopt?
d) Would one firm still be tempted to cheat in a cooperative equilibrium? Explain your answer.