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Answer for Game theory exercise

Soapy Inc and Suddies Inc are the only producers of soap powder. They collude and agree to
share the market equally. If neither firm cheat on the agreement, each makes $1 million profit.
If either firm cheat, the cheat makes a profit of $1.5 million, while the complier incurs a loss
of $0.5 million. If both cheats, they break even. Neither firm can monitor the other’s actions.
(a) What are the strategies in this game?
 Each firm has two strategies which is comply and cheat on the agreement.
(b) Construct the payoff matrix for this game
(c) What is the Nash equilibrium of this game?
 The Nash equilibrium is that both firms cheat and each makes $0 profit.
*Note: Remember previous lecture class, break even is equal to zero profit.