Reduced-RSS: Reduced Residual Search Space for Nash Bargaining Solutions

A fair and efficient resource allocation is crucial to maximize the efficiency of vehicular networks with time-varying resources among dynamically changing vehicles. The Nash Bargaining Solution (NBS) from the cooperative game theory has been one of the fair and optimal resource management solutions for multiple users. However, the computational complexity required to find the NBS for general utility functions exponentially increases either as the number of users increases or as the resources change over time. This is because the size of bargaining sets where the NBS should be found changes. In this paper, we propose an algorithm to reduce the size of the search spaces by considering the adjacent bargaining sets correlated by resource changes. We use the axiom of independence of linear transformations in NBS for the linear approximation of NBS in the adjacent bargaining sets based on its linear transform, leading to reduced residual search space. Moreover, we prove that the NBS is always included in the reduced residual search space based on the axiom of independence of irrelevant alternatives in NBS. Through simulations and experiments on synthetic and real traffic data, we demonstrate that the complexity of existing algorithms for NBS is lowered with the reduced residual search spaces.