Final answer:
The most feasible option for a cooperator is to not pay the cost of scrutiny because the expected payoff without paying for scrutiny is higher when considering risk and lack of guaranteed benefit.
Step-by-step explanation:
We can determine this by calculating the expected payoff of a cooperator when interacting with another member of the society.
The expected payoff for a cooperator without paying for scrutiny is:
Expected payoff = (Probability of interacting with a cooperator × Payoff from cooperator) + (Probability of interacting with a defector × Payoff from defector)
Expected payoff = (0.75 × 8) + (0.25 × 0) = 6 units.
If we subtract the cost of scrutiny, which is 2 units, from the expected payoff, we get:
Net payoff after scrutiny cost = Expected payoff - Cost of scrutiny
Net payoff after scrutiny cost = 6 - 2 = 4 units.
Since the net payoff after paying the cost of scrutiny (4 units) is still positive, it seems that it may be beneficial to pay the scrutiny cost. However, if the cost were increased to 3 units, the net payoff would be 6 - 3 = 3 units, which is still positive. But there are no guarantees that the detection of defectors will always lead to interactions only with cooperators, nor is the cost of scrutiny leading to increased payoffs. Hence, it's not necessarily beneficial to pay the cost of scrutiny if it only maintains or decreases overall payoff without providing additional benefit.