Multiobjective interaction programming problem with interaction constraint for two players (Q1955000)

Summary: We extend an existing cooperative multi-objective interaction programming problem with interaction constraint for two players (or two agents). First, we define an \(s\)-optimal joint solution with weight vector to a multi-objective interaction programming problem with interaction constraint for two players and get some properties of it. It is proved that the \(s\)-optimal joint solution with weight vector to the multi-objective interaction programming problem can be obtained by solving a corresponding mathematical programming problem. Then, we define another \(s\)-optimal joint solution with weight value to multi-objective interaction programming problem with interaction constraint for two players and get some of its properties. It is proved that the s-optimal joint solution with weight vector to multi-objective interaction programming problem can be obtained by solving a corresponding mathematical programming problem. Finally, we build a pricing multi-objective interaction programming model for a bi-level supply chain. Numerical results show that the interaction programming pricing model is better than Stackelberg pricing model and the joint pricing model.