Asymptotic Existence of Proportionally Fair Allocations

Fair division has long been an important problem in the economics literature. In this note, we consider the existence of proportionally fair allocations of indivisible goods, i.e., allocations of indivisible goods in which every agent gets at least her proportionally fair share according to her own utility function. We show that when utilities are additive and utilities for individual goods are drawn independently at random from a distribution, proportionally fair allocations exist with high probability if the number of goods is a multiple of the number of agents or if the number of goods grows asymptotically faster than the number of agents

The Core of the Participatory Budgeting Problem

In participatory budgeting, communities collectively decide on the allocation of public tax dollars for local public projects. In this work, we consider the question of fairly aggregating the preferences of community members to determine an allocation of funds to projects. This problem is different from standard fair resource allocation because of public goods: The allocated goods benefit all users simultaneously. Fairness is crucial in participatory decision making, since generating equitable outcomes is an important goal of these processes. We argue that the classic game theoretic notion of core captures fairness in the setting. To compute the core, we first develop a novel characterization of a public goods market equilibrium called the Lindahl equilibrium, which is always a core solution. We then provide the first (to our knowledge) polynomial time algorithm for computing such an equilibrium for a broad set of utility functions; our algorithm also generalizes (in a non-trivial way) the well-known concept of proportional fairness. We use our theoretical insights to perform experiments on real participatory budgeting voting data. We empirically show that the core can be efficiently computed for utility functions that naturally model our practical setting, and examine the relation of the core with the familiar welfare objective. Finally, we address concerns of incentives and mechanism design by developing a randomized approximately dominant-strategy truthful mechanism building on the exponential mechanism from differential privacy

Fairly Allocating Contiguous Blocks of Indivisible Items

In this paper, we study the classic problem of fairly allocating indivisible items with the extra feature that the items lie on a line. Our goal is to find a fair allocation that is contiguous, meaning that the bundle of each agent forms a contiguous block on the line. While allocations satisfying the classical fairness notions of proportionality, envy-freeness, and equitability are not guaranteed to exist even without the contiguity requirement, we show the existence of contiguous allocations satisfying approximate versions of these notions that do not degrade as the number of agents or items increases. We also study the efficiency loss of contiguous allocations due to fairness constraints.Comment: Appears in the 10th International Symposium on Algorithmic Game Theory (SAGT), 201

Statistical Multiplexing and Traffic Shaping Games for Network Slicing

Next generation wireless architectures are expected to enable slices of shared wireless infrastructure which are customized to specific mobile operators/services. Given infrastructure costs and the stochastic nature of mobile services' spatial loads, it is highly desirable to achieve efficient statistical multiplexing amongst such slices. We study a simple dynamic resource sharing policy which allocates a 'share' of a pool of (distributed) resources to each slice-Share Constrained Proportionally Fair (SCPF). We give a characterization of SCPF's performance gains over static slicing and general processor sharing. We show that higher gains are obtained when a slice's spatial load is more 'imbalanced' than, and/or 'orthogonal' to, the aggregate network load, and that the overall gain across slices is positive. We then address the associated dimensioning problem. Under SCPF, traditional network dimensioning translates to a coupled share dimensioning problem, which characterizes the existence of a feasible share allocation given slices' expected loads and performance requirements. We provide a solution to robust share dimensioning for SCPF-based network slicing. Slices may wish to unilaterally manage their users' performance via admission control which maximizes their carried loads subject to performance requirements. We show this can be modeled as a 'traffic shaping' game with an achievable Nash equilibrium. Under high loads, the equilibrium is explicitly characterized, as are the gains in the carried load under SCPF vs. static slicing. Detailed simulations of a wireless infrastructure supporting multiple slices with heterogeneous mobile loads show the fidelity of our models and range of validity of our high load equilibrium analysis

Approximate Maximin Shares for Groups of Agents

We investigate the problem of fairly allocating indivisible goods among interested agents using the concept of maximin share. Procaccia and Wang showed that while an allocation that gives every agent at least her maximin share does not necessarily exist, one that gives every agent at least $2/3$ of her share always does. In this paper, we consider the more general setting where we allocate the goods to groups of agents. The agents in each group share the same set of goods even though they may have conflicting preferences. For two groups, we characterize the cardinality of the groups for which a constant factor approximation of the maximin share is possible regardless of the number of goods. We also show settings where an approximation is possible or impossible when there are several groups.Comment: To appear in the 10th International Symposium on Algorithmic Game Theory (SAGT), 201

Mixed sharing rules

It is wellknown that a group of individuals contributing to a joint production process with diminishing returns will tend, in equilibrium, to put in too little effort if shares of the output are exogenous, and will put in too much effort if their shares are proportional to their inputs. We consider 'mixed' sharing rules, in which some proportion of the output will be shared exogenously, and the rest proportionally. We examine the efficiency properties of such rules, compare them with serial sharing rules, and suggest a sharing game whose noncooperative equilibrium is, in certain circumstances, Pareto efficientsurplus sharing, cost sharing, aggregative games