We consider the problem of dividing limited resources to individuals arriving over $T$ rounds. Each round has a random number of individuals arrive, and individuals can be characterized by their type (i.e. preferences over the different resources). A standard notion of 'fairness' in this setting is that an allocation simultaneously satisfy envy-freeness and efficiency. The former is an individual guarantee, requiring that each agent prefers their own allocation over the allocation of any other; in contrast, efficiency is a global property, requiring that the allocations clear the available resources. For divisible resources, when the number of individuals of each type are known upfront, the above desiderata are simultaneously achievable for a large class of utility functions. However, in an online setting when the number of individuals of each type are only revealed round by round, no policy can guarantee these desiderata simultaneously, and hence the best one can do is to try and allocate so as to approximately satisfy the two properties. We show that in the online setting, the two desired properties (envy-freeness and efficiency) are in direct contention, in that any algorithm achieving additive counterfactual envy-freeness up to a factor of $L_T$ necessarily suffers a efficiency loss of at least $1 / L_T$. We complement this uncertainty principle with a simple algorithm, HopeGuardrail, which allocates resources based on an adaptive threshold policy and is able to achieve any fairness-efficiency point on this frontier. In simulation results, our algorithm provides allocations close to the optimal fair solution in hindsight, motivating its use in practical applications as the algorithm is able to adapt to any desired fairness efficiency trade-off.
翻译:我们考虑的是将有限的资源分给抵达超过美元回合的个人的问题。 每回合都有随机数量的个人抵达,个人可以以其类型(即对不同资源的偏好)为特征。 在这种背景下,“公平”的标准概念是,分配同时满足嫉妒的无情和效率。前者是个人保障,要求每个代理商更愿意自己分配,而不是任何其他代理商的分配;相反,效率是一种全球财产,要求分配能够清除可用资源。对于可变资源而言,当每个类型个人的数量在先已知的公平性时,上述偏差可以同时用于大型公用事业功能。然而,在网上设置中,当每类个人的数量只是一轮地披露时,“公平”的一个标准概念是“公平性”概念,即分配时不能同时保证这些偏差和效率。 前者是个人保证,要求每个代理商更愿意自己分配自己的资源,以大致满足这两个属性。 而在网上设置中,两种理想的(自由和效率和效率)是直接争议的,在任何算法中,实现最不真实的不合理性、最接近性、最接近性、最接近性、最接近于理想性的成本的计算值的计算,在1美元-T的资源上,一个效率上,一个效率是我们以1美元的汇率分配一个效率为标准上的效率。