Using a particle swarm optimization approach to examine a competitive production situation constrained by sustainable levels of pollution

This paper presents an algorithmic approach to determine an equilibrium solution to a non-cooperative duopoly game where sustainable pollution constraints exist. In contrast to an analytical approach, which typically requires simplifying assumptions such as linear demand and linear cost functions, we use a composite particle swarm optimization technique to determine the equilibrium values. This approach has the advantage that it can deal with and find optimum values for non-linear functions. In the paper we specifically include production constraints due to pollution. We solve a benchmark problem and compare the results obtained from particle swarm optimization approach with those obtained analytically thus demonstrating that the algorithmic approach is resilient and rigorous.