Final answer:
The question concerns using game theory to devise an algorithm for determining the minimum effective bribe in a scenario resembling a prisoner's dilemma. Firms A and B must choose between collusion and cheating, and must use cost-benefit analysis considering the potential gains and losses to decide the optimal strategy. The best strategy, suggested by the analysis, is likely to be collusion for both firms.
Step-by-step explanation:
To determine the minimum effective bribe using an optimal strategy that uses the smallest total amount of cash, we can refer to game theory concepts, notably the prisoner's dilemma, in which individuals assess the benefits and risks of cheating versus cooperating. In this context, two firms, Firm A and Firm B, are considering whether to collude or cheat. The scenario implies a cost-benefit analysis, where each firm evaluates potential gains against potential losses.
Firm A, being the larger entity, makes a profit of $1000 if neither firm cheats. If Firm A cheats while Firm B doesn't, it can only increase its profit marginally, because Firm B is smaller. However, if Firm B cheats and Firm A notices, it will react by cheating as well, causing Firm B to lose 90% of its gains. If both firms cheat, Firm A loses at least 50% of what it could have earned. Considering these dynamics, the best outcome for both firms is to collude, as the potential gain from cheating is minimal for Firm A, and the risk of being caught and retaliated against is high for Firm B.