Abstract
We extend a standard two-person, non-cooperative, non-zero sum, imperfect inspection game, considering a large population of interacting inspectees and a single inspector. Each inspectee adopts one strategy, within a finite/infinite bounded set of strategies returning increasingly illegal profits, including compliance. The inspectees may periodically update their strategies after randomly inter-comparing the obtained payoffs, setting their collective behaviour subject to evolutionary pressure. The inspector decides, at each update period, the optimum fraction of his/her renewable budget to invest on his/her interference with the inspectees’ collective effect. To deter the inspectees from violating, he/she assigns a fine to each illegal strategy. We formulate the game mathematically, study its dynamics and predict its evolution subject to two key controls, the inspection budget and the punishment fine. Introducing a simple linguistic twist, we also capture the corresponding version of a corruption game.
Highlights
An inspection game consists of a game-theoretic framework, modelling the non-cooperative interaction between two strategic parties, called inspector and inspectee; see, e.g., [1,2] for a general survey
We study the spread of illegal activity in a population of myopic inspectees interacting under the pressure of a short-sighted inspector
We investigate the spread of corruption in a population of myopic bureaucrats interacting under the pressure of an incorruptible supervisor
Summary
An inspection game consists of a game-theoretic framework, modelling the non-cooperative interaction between two strategic parties, called inspector and inspectee; see, e.g., [1,2] for a general survey. Avenhaus and Kilgour [21] introduced a non-zero-sum, imperfect (Type 2 error) inspection game, where a single inspector can continuously distribute his/her effort-resources between two non-interacting inspectees, exempted from the simplistic dilemma whether to inspect or not.
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