Given that you may lie or tell the truth, and other applicants may do the same. The 'game' consists of three rounds, initial selection, background check and the interview. The employer may check or not check after a winner is selected, but lets assume that once the 'winner' is chosen further checkign will not be performed unless the 'winner' is not performign their job, in which case checking will only confirm what teh employe already knows, that teh winner, regardless of whether they pass teh check or not is not performing. i.e. termination.
From the point fo view of the player, the object of the first stage (selection) is to get to the third stage (interview). Since the HR typically limits the number of winners at this stage (i.e. they weed out the less qualified candidates prior to doign any checking), the players must compete with one another to win one of these spots. The losers get nothing. So assuming an average player. If the average player tells the truth, and all other players tell teh truth, they have a 50% chance fo being chosen for round 2. If the player choses to lie and the other players tell teh truth they have a 100% chance of being chosen, if they tell the truth and all other players lie then they have 0% chance of beign chosen. Therefor there is good reason to lie, and no reason to tell the truth at this stage.
The only thing that can guarantee honesty in the players is if every HR checks every resume before the selection process, or in the least continues checking resumes until all apparently qualified candidates have been checked. Given that people are unlikely to lie and make themselves appear less qualified.
Now this presents itself as another game. HR's compete with one another over employees, i.e. the HR wins by selecting valid players before they are selected by other HR's. It takes longer to check a candidate than to not check a candidate. Therefor checkign the candidate, while reducing the risk of gettign an unqualified applicant, increases the risk that the applicant will be hired by another company before the check is finished.
So you really have a 6 person game. Crystal, Leroy, Rupert and Dick are the players and Alice and Bob are the HR's.
Crystal and Leroy are equally qualified. 1.0 true resume value.
Dick and Rupert are unqualified. 0.0 true resume value.
Crystal and Rupert tell the truth. +0.0 apparent resume value
Leroy and Dick lie. +1.0 apparent resume value
Crystal - Resume value 1.0
Leroy - Resume value 1.0 apparent resume value 2.0
Dick - Resume value 0.0 apparent resume value 1.0
Rupert - Resume value 0.0
Alice does not check.
Bob does check.
The interviews take 1 day per person and the check takes 1 day to complete before an interview can be made. The job is offered or not as part of the interview. Assume both jobs are equal and a candidate will accept the first offer made to them.
Both Alice and Bob dismiss Rupert out of hand as his resume is unqualified.
Alice offers Leroy a job as he appears competant in the interview. (apparent resume value 2.0, backed by true value of 1.0)
Bob checks Leroy's resume (apparent resume value 2.0) and finds he lied (1.0).
Bob cannot interview Leroy(1.0) so he checks crystal/dick.
Alice randomly interviews either Crystal or Dick (1.0/1.0). She offers Alice a job, but not Dick. she gains 0.5 from Crystal and 0.0 from dick (half their existing true value
Bob Interviews Crystal if she was nto chosen on day 2 and if she choses his interview first. He gains 0.25 as half of her remaining true value.
Alice Interviews Crystal/Dick, gaining half of crystals remaining value and half of dicks for 0.25.
So Alice gained 1.75 qualified employees while Bob gained only 0.25
Therefor, for the HR, it is 7 time more effective to NOT check resumes than it is to check them, assuming the interview will show which candidates are really qualified.
It is completely irrelevant whether the player gets caught because the interview would already have landed the liar a job from a non-checker before it has a chance to cost him a job from the checker.
The actual scores depend on the actual values of interview time, check time, and the efficiency of the interview to select candidates. You could expand it to include a range of interview efficencies, and also compensate for on the job effectiveness and the effects of some players lying more than others and for the efficiency of the check process itself (job performance efficiency versus verifiable 'qualification').