Design for contract mechanism of acceptance sampling plans based on two-person game

Traditionally, acceptance sampling plans are two-person decision process, which is used to check whether the reliability of the producer's product meets the requirements of the consumer. However, during the two-person decision process, the producer, as a rational person, tends to use less resources for the sampling plans to save the costs and promote the acceptance of the product, while the consumer who also acts as a rational person tends to use more so as to test the reliability of the product as realistically as possible and reduce the loss caused by defective product. Therefore, the conflict of interest between the producer and consumer exists in determining the acceptance sampling strategies. In this paper, firstly, the contract mechanism for acceptance sampling plans is proposed for the conflict of interest between them, and then the two-person game model between the producer and the consumer is constructed from the three dimensions including game participants, strategy spaces and payoff functions to obtain the acceptance sampling strategies conforming to the results of Nash equilibrium. Finally, the numerical case is given to show the balance of acceptance resources and the relative optimality of costs after the game, which solves the problem of conflicts of interest in the acceptance sampling plans.