Price of Fairness for allocating a bounded resource

Abstract

In this paper we study the problem of allocating a scarce resource among several players (or agents). A central decision maker wants to maximize the total utility of all agents. However, such a solution may be unfair for one or more agents in the sense that it can be achieved through a very unbalanced allocation of the resource. On the other hand fair/balanced allocations may be far from optimal from a central point of view. So, in this paper we are interested in assessing the quality of fair solutions, i.e. in measuring the system efficiency loss under a fair allocation compared to the one that maximizes the sum of agents utilities. This indicator is usually called the Price of Fairness and we study it under three different definitions of fairness, namely maximin, Kalai-Smorodinski and proportional fairness.Our results are of two different types. We first formalize a number of properties holding for any general multi-agent problem without any special assumption on the agents utilities. Then we introduce an allocation problem, where each agent can consume the resource in given discrete quantities (items). In this case the maximization of the total utility is given by a Subset Sum Problem. For the resulting Fair Subset Sum Problem, in the case of two agents, we provide upper and lower bounds on the Price of Fairness as functions of an upper bound on the items size.

Price of fairness in two-agent single-machine scheduling problems

“…Indeed, one can always define the NBS as the one maximizing such product (see, e.g., Agnetis, de Pascale, and Pranzo (2009)), yet the existence of an NBS does not guarantee that there is a proportionally fair solution. On the other hand, one can show that if a proportionally fair solution exists, then it is unique (Nicosia, Pacifici, and Pferschy, 2017). Clearly, the latter general property holds true also in our scheduling setting.…”

“…Bertsimas, Farias, and Trichakis (2011) focus on proportional fairness and max-min fairness and provide a tight characterization of PoF for a broad family of allocation problems with compact and convex utility sets of the agents. Nicosia, Pacifici, and Pferschy (2017) establish a number of properties for the PoF, which hold for any general multi-agent problem without any special assumption on the agents' utilities, focusing on max-min, Kalai-Smorodinsky and proportional fairness. Situations in which the agents pursue the minimization of their costs (rather than maximization of their utilities) have been dealt with by Ertogral and Wu (2000), who derive a measure of fairness among a set of supply chain members.…”

Sharing Economy Platforms’ Pricing Strategies and Decision Preferences: The Example of DiDi

“…Depending on the types of idle resources shared via the sharing economy platform, the variable costs of providers will be different (Nicosia et al, 2017).…”

Equity in genetic newborn screening

“…A small number of states address the equity issue through heuristic approaches, in an effort to balance the false negative rates in different groups; for example, California's CF panel is designed to ensure a minimum sensitivity for each select group (Kharrazi et al, 2015; Sontag, Wright, James Beebe, & Sagel, 2009). A panel that is equitable among groups, for example, in terms of false negative rates, may lead to an increase in the false negative rate in the general population, that is, there is a price of equity (e.g., Bertsimas, Farias, & Trichakis, 2011; Nicosia, Pacifici, & Pferschy, 2017).…”