The Decision of the Product's Performance Margin and Reliability: An Evolutionary Game Perspective

In product trading, the buyer generally wants a product with higher reliability, which will increase the seller's cost. As a result, there exists the buyer-seller game about the product's reliability. Nowadays, most studies just introduced a general concept of "reliability level" when modeling the buyer-seller game, but not further explored the meaning and origin of reliability. Therefore, they cannot effectively describe and forecast the seller's action and the buyer's appeal to influence the product's reliability. According to the basic definition, reliability essentially evaluates whether the function achievement of a product can meet its requirement, which can be further quantified by specific performance. Therefore, the product's reliability derives from the product's performance supplied by the seller and the buyer's requirement, and can be calculated by the probability that the product's performance margin is greater than 0. On this basis, in this work, a buyer-seller game model for the product's performance margin and reliability is proposed, aiming to predict and guide the buyer's and seller's behaviors. For this game, the buyer's strategy is the performance threshold representing the requirement for the product, and the seller's strategy is the product's performance. In the game model, the performance threshold profit, the performance cost, and the failure risks are introduced to quantify the payoffs of both sides. Evolutionary game theory is adopted to model the dynamics of strategy evolution and solve the stable strategy. Finally, the phase transition of different game results with the change in payoffs can be clarified. The case of a two-strategy game indicates that the proposed method can predict the both sides' actions under different payoffs; also, the guidance can be provided to promote the buyer-seller cooperation.

Keywords: Reliability, Buyer-seller game, Performance margin, Evolutionary game theory, Phase transition, Cooperation.