Incorporating monitoring technology and on-site inspections into an n-person inspection game

A two-stage game between an inspector and multiple inspectees is modeled in which the inspector may choose to invest in a monitoring technology in the first stage to supplement the inspector's subsequent inspection strategy in the second-stage simultaneous game. The game is motivated by an environmental regulator that has a limited budget for monitoring and inspecting several industrial enterprises, each with an incentive to pollute. A monitoring technology may alter the payoffs of the second-stage game, by making inspection more efficient and by altering the inspectees’ payoffs so as to increase the effect of deterrence. Computation of Nash equilibria is challenging for nonzero sum games in general and also challenging in our case as the utility function of the inspector is nonconcave in its actions. Using the special structure of our game we develop an algorithm to efficiently determine Nash equilibria. We then derive some managerial insights by applying the algorithm to several examples and examining the Nash equilibria, including a counterintuitive outcome that the addition of monitoring technology may cause more inspectees to pollute than would otherwise.