Characterization of envy free solutions for queuing problems

Abstract

In this study we are working on queuing problems. In our model a solution to a queuing problem is an ordering of agents and a transfer vector where the sum of the transfers of agents is equal to zero. Hence a queuing problem is a double, where we have a finite set of agents and a profile of payoff functions of agents which represent their preferences on their orderings and transfers. We are assuming that the payoff functions of agents are quasi-linear on transfers. Our main aim is to find envy free solutions for queuing problems. Since payoff functions of agents are quasi-linear envy freeness implies Pareto efficiency. For problems where there are less than five agents, we show that the set of envy free solutions is not empty and we are able to characterize the envy free solutions. We conjecture that our results may be extended to general case similar to our extension from three person case to four person case. When we assume that a queuing problem satisfies order preservation property we are able to characterize envy free solutions with a solution concept that we introduce in this study.