Mathematics behind Incentive Design I was working on an Applied Math project on allocation and I had an interesting idea about extending it to providing incentives to different "players" in the allocation process. But I am clueless about **how** incentives are designed. For instance, if I had 2 tickets to a football game and 5 people that I am trying to allocate to (2 get 1 each), how do I provide incentives for someone who doesn't really want to go to say no and stuff (basically, ensure that the "best" 2 actually get the tickets). I just want to know where should I get started on reading about this. I understand this is probably under Game Theory and probably a subpart of Mechanism Design but is there a specialized field of Math/Econ for designing incentives?

I believe the area you are interested in is Information Economics.

There is a subpart of information economics, called Screening. Screening is essentially about how an uninformed agent can get an informed agent to provide truthful information about themselves.