Final answer:
The question involves business strategy and game theory, considering how two firms (Firm A and Firm B) must decide whether to trust each other based on profit scenarios where cheating could either benefit or cost them immensely. The scenario requires understanding the potential outcomes of different strategies and their consequences on profits.
Step-by-step explanation:
The question pertains to business strategy and game theory, specifically about how two firms can choose whether to trust each other under certain profit scenarios. First, let's consider Firm A's situation. If Firm A believes that Firm B will cheat on their agreement by increasing output, Firm A will also increase output as this results in a $400 profit compared to a $200 profit if Firm A does not cheat and Firm B does. However, Firm A must consider that if both firms cheat, the profit could decline substantially.
For Firm B, the situation is slightly different. If Firm B cheats and Firm A does not notice, Firm B will double its money. But if Firm A does notice and also cheats, then Firm B could lose 90% of its profit. This creates a dilemma because trusting Firm A could lead to a stable but possibly smaller profit, while cheating could either double their profit or result in a significant loss depending on Firm A's reaction.
The example you provided regarding the venture capitalist and the software company, hardware company, and biotech firm relates to the construction of probability distribution functions (PDF) for each investment option based on their profit chances and outcomes. However, this is a separate scenario pertaining to investment risk analysis, which also relates to business and financial decision-making processes.