(untitled) (Advances in Systems Science and Applications, 2022)
We investigate a problem of searching for Pareto equilibrium sets of an insurance rate and an industrial damage utilization price. We consider a system, which, in the case of industrial accidents, arises around an industrial firm. An industrial firm, a waste utilization firm, and an insurance company are considered as the system’s agents. We develop profit functions for the agents, and we determine compromise prices on waste utilization and insurance, which provide the system’s stability. We analyze the set of industrial risk control systems with a various number of the agents and the agent’s relations. A problem of determining an optimal solution is solved on the basis of maximizing agents’ profit functions. The sets of an equilibrium industrial damage utilization price and an equilibrium insurance rate are defined as Pareto equilibrium. A problem of determining the set of an insurance rate is solved taking into account constraints according to requirements of an industrial firm and an insurance company. A problem of determining the set of an industrial damage utilization price is solved taking into account constraints according to requirements of an industrial firm and a waste utilization firm. We consider the following models of industrial risk control systems: agents have a strong relation and a weak relation, additionally, one agent of each type and of many agents of the same type.