incentive compatability means a mechanism where the best outcome for each person is achieved when they say the truth.

consider insurance. insurance has the problem of adverse selection. the people who want to buy insurance the most are those who have risky livestyles. insurance companies cannot know with perfection which person is low risk and which is high risk. this leads to even low risk people having to pay high premiums.

in this case, if i’m a risky person, my incentive is to lie. if i say the truth, i’ll have to pay higher premium.

consider first price auctions. in first price auctions, everyone submits a bid. the person with the highest bid wins and has to pay the amount they bid. so lets say a product is on auction and my value for the product is 100rs. if I bid 100rs, even if I win, my payoff is 0. my payoff will be positive only when I can get the product for less than its value. so i underbid. first price auctions are not incentive compatible.

on the other hand, consider second price auctions. in these, everyone submits a bid as earlier. the person with the highest bid wins but has to pay the second highest bid. so suppose 3 people took part and bid 60,70 and 90. the person who bid 90 will win but has to pay only the second highest bid 70. this mechanism is incentive compatible. the dominant strategy for any person is to bid the correct value. if they win (assuming no tie), they get a payoff > 0.

game theory is interesting.