Nash Equilibria in a Multiple Stage Inspection Game

An inspection game is a mathematical model of a situation where an inspector verifies that another party, called inspectee, adheres to certain legal rules. This paper will consider a model with one inspector and n inspectees and investigate the Nash equilibria of a multiple stage inspection game given a budget allocation. The inspector I sets a “target level” for budget allocation of each inspectee Pi. The inspector decides to allocate percentage of the target level to n inspectees who work non cooperatively. In each inspection time, computations of Nash equilibria is presented. There are three cases for the inspector's budget in relation to the sum of the target levels for the inspectees. The paper will show that only the case with budget more than the sum of target levels of all inspectees can be extended into a multiple stage inspection game.