Inspection games in a mean field setting

In this paper, we present a new development of inspection games in a mean field setting. In our dynamic version of an inspection game, there is one inspector and a large number N interacting inspectees with a finite state space. By applying the mean field game methodology, we present a solution as an epsilon-equilibrium to this type of inspection games, where epsilon goes to 0 as N tends to infinity. In order to facilitate numerical analysis of this new type inspection game, we conduct an approximation analysis, that is we approximate the optimal Lipschitz continuous switching strategies by smooth switching strategies. We show that any approximating smooth switching strategy is also an epsilon-equilibrium solution to the inspection game with a large and finite number N of inspectees with epsilon being of order 1/N

Quality and Environmental Regulation: Verifying Compliance along the Supply Chain

Among the factors providing incentives to monitor the behaviour of input suppliers are the regulatory requirements to which downstream firms are subject. We develop a formal economic model to examine the relationship between the strictness of the regulatory environment and downstream firms’ incentives to act as inspectors of their sub-contractors. We consider the interaction between a downstream producer and an upstream input supplier. The downstream chooses the probability with which to monitor the upstream’s compliance and the upstream chooses a compliance level which determines compliance of the end product with quality or environmental regulation. We find that the strictness of regulation affects the downstream’s monitoring strategy in combination with the level of quality or environmental standards. If the standards are sufficiently low then the strictness of regulation increases incentives to monitor the upstream. Contrary, if the standards are sufficiently high then the pressure on the downstream to monitor the upstream is relaxed and the strictness of regulation decreases incentives to monitor. We argue that the strictness of regulation should not be treated in isolation as a factor determining the choice of downstream firms to monitor their input suppliers.compliance; monitoring; supply chain; quality and environmental regulation

Game-theoretic analysis of the quality assurance problem in a two-echelon supply chain with a retailer as the quality gatekeeper

We consider a two-level supply chain involving a manufacturer and a retailer who serves as the quality gatekeeper. The manufacturer determines a wholesale price and a defective rate and announces his decisions to the retailer, who then makes her decisions on the retail price and identification rate that means the percent- age of the defects identified by the retailer and reflects the retailer’s gatekeeping effort on her quality assurance. We accordingly develop a leader-follower game and solve it to find Stackelberg equilibrium for the manufacturer and the retailer. In order to examine whether or not the supply chain benefits from the retailer\u27s quality gatekeeping effort, we also develop and solve another leader-follower game where the manufacturer still announces its wholesale pricing and defective rate decisions but the retailer only decides on the retail price. We show that the manufacturer’s equilibrium defective rate for the game with the retailers gate-keeping is higher than that for the game without the retailer’s gatekeeping. The ratio of the manufacturers profit to the retailer’s profit is increased when the retailer serves as the gatekeeper. Moreover, the retailer reduces her price when she acts as the gatekeeper, if and only if the supply chain-wide cost decreases as a result of the retailer’s gatekeeping effort. We also perform sensitivity analysis of each parameter in our game models to further examine the impacts of the retailer’s gatekeeping on the manufacturer’s and the retailer’s decisions and profits. We find that the retailer’s penalty cost per defect has more significant impacts than the manufacturer’s unit penalty cost. The paper ends with a summary of managerial insights