Public bad conflicts: Cyclical Nash strategies and Stackelberg solutions

The first purpose of this paper is to study the dynamics of a general socially undesirable public evil and the possibility of cyclical Nash strategies in equilibrium. As a second result of the paper we found the analytical solutions of the hierarchical (Stackelberg) game for the public bad accumulation model. In both cases we use the differential game modeling, as the appropriate tool for the economic analysis that follows. The control setting is not the usual one, which assumes an accumulated stock of a public bad (e.g. pollutants, wastes or even tax evasion), but we claim that the disadvantage which is responsible for the unwished public evil accumulation is the use of the available inputs and equipment. Therefore, this could be a crucial assumption which possibly prevents the irreversibility of the public bad accumulation. As a continuation, we set as stock the available resources (inputs plus equipment) and the stress of the regulator is to reduce these resources. In the first case of Nash equilibrium, we find that the establishment of cyclical strategies, during the game between the agents in charge and the regulator, requires that the agents’ discount rate must be greater than the government’s discount rate, i.e., the agents in charge must be more impatient than the government (acting as the regulator). In the second case of the hierarchical setting, we provide the analytical expressions of the strategies as well as the steady state value of the resources’ stock. We use the notion of a public bad as the opposite meaning to the public good.