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 compiler incurs a loss of $0.5 million. If both cheat, they break even. Neither firm can monitor the other's action.

1. What are the strategies in the game?
2. What is the equilibrium of the game if played once?
3. Is the equilibrium a dominant-strategy equilibrium?