Many-player inspection games in networked environments

In communication architectures, nodes are expected to spend their own resources so as to relay other nodes´ messages or perform other services for the common good. However any selfish node, if given the opportunity, would typically prefer - to spare its own resources - to avoid serving the other nodes. This creates a potential problem to any collaborative protocol. A possible approach towards this issue consists in performing audits on the actions of the individual nodes, and applying some form of sanction to those whose misbehaviour has been detected during an inspection. However typically, auditing is costly and due to limited resources it can be carried on only on a sampling basis. It is clear that the rate of inspection has to be adapted to the rate of misbehavior, so as to strike a balance, from the point of view of the inspector, between the audit costs and the avoided damage to the system. Since the misbehaviour rate of rational agents is not predefined or fixed, but in turn depends from inspection rate, the overall behavior of the system made by inspectors and inspectees fits into a typical interdependent interaction landscape and can be modeled using Game Theory. The above described audit situation corresponds to a class of games known as Inspection Games. In this paper, we model several versions of Inspection Games (IGs), up to the most general case involving m inspectors and n inspectees. We resolve each game by computing the strategy that rational players would follow. Moreover, we also extend the IG model by taking into account the possibility of undetected violations, i.e. false negatives in the inspections.