Summary: Lot sizing and pricing is an important activity that appear in business. From the competitive view of a seller-buyer system, such pricing and inventory control problem is basically a two-person game in which both players try to maximize (or minimize) their individual gains (or costs). Most of the seller-buyer inventory games are analytics-oriented and are lack of a solution procedure. As a result, it will retard the application of these models. After modeling the seller-buyer system as a Stackelberg game, particle swarm optimization (PSO) algorithm combined with constrains handling technique based on symbiosis phenomenon in nature, are used to solve this constrained nonlinear optimization problem (CNOP). Symbiosis mechanism, which incorporates infeasible solutions into the population, makes PSO capable to better explore the search space and, finally, fmd the equilibrium results. Pricing, ordering, and backordering results are close to the exact solutions and provide valuable information to the seller and buyer. In light of its feasibility, the procedure could be extended to solve the cooperative inventory game in the future.