Research on the two-player two-way principal-agent model and optimization algorithm with lower and upper bounds

An optimization algorithm is designed for the solution of the two-way principal-agent model with lower and upper bounds. This work analyzed the two-way principal-agent relationship between the two players who both have dual status: the principal status and the agent status, then proposed the expected utility function for the virtual principal, and a two-way principal-agent model with lower and upper bounds which embodies two players and two-side constraints was established too, then the upper and lower bounds of the parameters are determined by the fixed point theorem, finally Pivoting algorithm and sequence of quadratic programming method were used to solve those models. The example indicated that it is necessary to balance the investment and return values of the alliance members to maximize the utility of the alliance and achieve real incentive for them by determining the appropriate reserved utility value.