The principal aim of this paper is to introduce the framework for a cooperative game theoretical approach to risk analysis using network structure. Probabilistic risk analysis (PRA) is a common methodology for evaluating risks associated with real-world network structure. Although there are numerous studies on PRA from a physical engineering perspective, Hausken (2002) noted that human behavior is a significant factor in estimating risk using PRA, and he integrated PRA and game theory. While his and related works focused on non-cooperative game theory, in some situations, such as chemical plants, cooperative structures are the norm. Therefore, we here provide a risk analysis method based on cooperative game theory, and especially so-called Shapley values.

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A model study was conducted to establish 2 feasible production and application systems for the long-term, sustained release of pheromone into the atmosphere of targeted areas. The desired goal of effective release was set at least half a year. 2-Ethylhexyl acetate (EHA) was selected as a pheromone analogue due to its similar structure and easier access for quantitative analysis. At first EHA was impregnated in wax particles, which were then encapsulated employing the complex coacervation of a gelatin-gum arabic system. The release period of EHA through the gelatin wall, however, turned out to be too short--only a week at most. As a second attempt, a modification of the two-phase emulsion technique was employed to encapsulate multiple numbers of wax particles in hydrated networks of gelatin. Though the initial release rate of EHA was still too high, 60 per cent of encapsulated EHA underwent sustained release over six months after absorbed moisture had completely evaporated. A two-step mechanism of mass transfer was proposed and the related parameters in terms of the capacity coefficient and effective diffusion coefficient were estimated.

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