In the conventional Stackelberg game, all players are perfect optimizers, able to choose the best responses to their competitors’ decisions. In contrast, in the Stackelberg game with bounded rationality, players are unable to optimize their individual payoffs and face strategic uncertainty due to the performance of competitors. In real games, players are usually unaware of the performance of their competitors. Therefore, to survive in the competitive market, they are forced to make decisions under conditions of bounded rationality. Due to the importance of decision-making in this situation, in this study, the Stackelberg game of deteriorating inventory within a two-level supply chain was developed considering the concept of bounded rationality. The follower in the Stackelberg game (manufacturer) is poorly aware of the leader’s performance in terms of order size. Therefore, she/he manufactures the products at rates with normal distribution. For the first time, an algorithm based on Bayesian conjugate pair was proposed to solve the Stackelberg game with bounded rationality for deteriorating products. In addition, a comparison was made between the above conditions and a mode in which the leader’s strategy is fully observable to the follower. The approach used in the proposed algorithm to adjust the production rate was also compared with the adjustment based on the partial adjustment model, and the obtained results prove the convergence of the proposed algorithm.
