Iterative cost update method of generalized Kelly mechanism for fair utility resource allocation

We consider a resource allocation problem that ensures a fair utility among selfish agents who share a divisible resource. When the available resource is limited and the required amount of the resource cannot be allocated to agents, resource management is an important issue in multiagent systems. If there are selfish agents who want to maximize their utilities, we must prevent their behavior to realize a fair resource allocation. In this paper, we propose a fair utility resource allocation mechanism based on the generalized Kelly mechanism. In the proposed mechanism, the resource allocation is determined by a resource manager (RM) based on the resource requests of all agents, and the resource allocation problem is formulated as a resource allocation game. In the resource allocation game, we show uniqueness of a fair utility resource allocation which satisfies that the corresponding resource request is a Nash equilibrium and is equal to the resource allocation. Moreover, we assume that RM cannot know the utility functions of agents, but can calculate their utilities after the resource allocation. Using these results, we introduce a cost update function which realizes the fair utility resource allocation. By using simulations, we demonstrate the effectiveness of the proposed mechanism.