Multi-Principal Multi-Agent Contract Design: Theory and Application to Device-to-Device Communications

Abstract

How to stimulate the devices to participate is a key problem in the device-to-device (D2D) communications, especially when there are multiple base stations in practice. On one hand, the base station needs to lower the price to compete with other base stations for attracting more devices. On the other hand, the base station needs to increase the price to obtain more benefit. In this paper, we propose an optimal multiprincipal multiagent contract design to tackle such a challenge. Specifically, we formulate the multiprincipal contract design problem as a game theoretic optimization problem, where the objective of each principle (base station) through contract design is to maximize its overall utility obtaining from the trade with agents (devices) subject to the individual rationality and incentive compatibility constraints. By solving the game theoretic optimization problems, we can obtain the equilibrium contract where the contracts of different principals reach an equilibrium and any deviation from a single principal will lead to the degradation of its own utility. Moreover, under the equilibrium, both the individual rationality and incentive compatibility constraints are satisfied, i.e., all agents will choose the corresponding contract according to their types to reach the optimal nonnegative utilities. Simulation results show that compared with the monoprincipal contract design, both the utilities of devices and the social welfare can be improved with the multiprincipal contract design.