in week 7 of Games and Information of NPTEL, the professor mentioned that additional information is not always useful. there can be games where additional information reduces the payoff.

intrigued by this idea, i asked gemini to provide more examples for it. and one of the examples it gave was the hirshleifer effect. the effect states that information reduces the total utility of a society by removing insurance.

consider this example - a hypothetical city has 5 banks and a group of robbers. the robbers rob 1 bank at random each year. to safeguard them from the losses, all 5 banks take up insurance. this distributes the risk from a single bank to each bank. suppose that this year the robbers declare that they’ll be robbing bank 2. this is additional information. the uncertainity is gone. but what has happened now is that because the other banks know that they are not going to be robbed this year, they do not take the insurance. afterall, why pay premium for an event that you know will not happen. so the end result is that bank 2 has to bear all the cost of the robbery.

the additional information - which decreased the uncertainity, caused potential insurance buyers to not take the policy.