Inspection games with local and global allocation bounds

Abstract

This article discusses a two-player noncooperative nonzero-sum inspection game. There are multiple sites that are subject to potential inspection by the first player (an inspector). The second player (potentially a violator) has to choose a vector of violation probabilities over the sites, so that the sum of these probabilities do not exceed one. An efficient method is introduced to compute all Nash equilibria parametrically in the amount of resource that is available to the inspector. Sensitivity analysis reveals nonmonotonicity of the equilibrium utility of the inspector, considered as a function of the amount of resource that is available to it; a phenomenon which is a variant of the well-known Braess paradox.

Non‐zero‐sum nonlinear network path interdiction with an application to inspection in terror networks

“…In our general setting, we find that the smuggler's Nash equilibrium strategy is one that equates the marginal utilities of allocating the inspection resources between different arcs. This property of the Nash equilibrium smuggler strategy resembles and extends that encountered in other twoplayer inspection and defender-attacker games [7,24], where the supports of Nash equilibrium strategies equal one another for the two players.…”

“…The intuition of the result of Theorem (7) is similar to that of other two‐player non‐zero inspection and defender‐attacker games in which the inspector (or defender) prioritizes inspection sites according to the inspectee's payoff. The inspectee chooses where to violate and so the inspectee payoffs (as well as the inspector's budget) dictate the support of the Nash equilibrium strategies.…”

Multiple agents finitely repeated inspection game with dismissals

“…The game modeled in this paper is an extension of previous research (Deutsch et al 2011(Deutsch et al , 2013. In Deutsch et al (2011), the authors model a single-stage inspection game between a single inspector and several independent agents.…”

“…In Deutsch et al (2013), the authors consider a single-stage inspection game between a single inspector and a single agent with some known locations where the players can act. The inspector has a finite resource for its inspections.…”

“…For an extended summary of previous literature on inspection games, we refer the reader to the literature reviews in Deutsch et al (2011Deutsch et al ( , 2013, or other literature surveys in this area (e.g., Avenhaus et al 2002). Here, we will review some relevant and recent research done in the area of inspection games.…”