Question: If Soapy Inc. and Suddies Inc. play the game in Problem 5 repeatedly, on each round of play:
a. What strategies might each firm adopt?
b. Can the firms adopt a strategy that gives the game a cooperative equilibrium?
c. Would one firm still be tempted to cheat in a cooperative equilibrium? Explain your answer.
Problem 5
Soapy Inc. and Suddies Inc., the only soap- powder producers, collude and agree to share the market equally. If neither firm cheats, each makes $1 million. If one firm cheats, it makes $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. If the game is played only once what is the equilibrium? Is it a dominant-strategy equilibrium? Explain.