Car is having engine troubles.
Took it to the dealership.
Saw signs for Lojack.
Lojack doesn't advertise on the products they protect.
1) It's easy to create a false signal: a non-customer could put a sticker in the window. The game theoretical outcome erodes the credibility of the signal.
2) Good for business to catch a thief for real. Fewer thieves stealing cars, more apt to attract new customers at the dealership.
Note: the social outcome should be (ceteris paribus) fewer auto thefts. Positive externality. Standard economic theory predicts that this service will be under-supplied in the marketplace because people have an incentive to free-ride.
How strong do you suppose the free-rider effect is here? What factors might mitigate it? Is Lojack undersupplied? How would you test that hypothesis?