Papers

Given an initial resource allocation, where some agents may envy others or where a different distribution of resources might lead to higher social welfare, our goal is to improve the allocation without reassigning resources. We consider a sharing concept allowing resources being shared with social network neighbors of the resource owners. To this end, we introduce a formal model that allows a central authority to compute an optimal sharing between neighbors based on an initial allocation. Advocating this point of view, we focus on the most basic scenario where a resource may be shared by two neighbors in a social network and each agent can participate in a bounded number of sharings. We present algorithms for optimizing utilitarian and egalitarian social welfare of allocations and for reducing the number of envious agents. In particular, we examine the computational complexity with respect to several natural parameters. Furthermore, we study cases with restricted social network structures and, among others, devise polynomial-time algorithms in path- and tree-like (hierarchical) social networks.

poster session 1 @ blue 6, poster session 12 @ blue 6, oral session 1 @ blue 6, poster session 1, poster session 12, oral session 1

We study the problem of allocating indivisible goods among strategic agents. We focus on settings wherein monetary transfers are not available and each agent's private valuation is a submodular function with binary marginals, i.e., the agents' valuations are matroid-rank functions. In this setup, we establish a notable dichotomy between two of the most well-studied fairness notions in discrete fair division; specifically, between envy-freeness up to one good (EF1) and maximin shares (MMS). First, we show that a Pareto-efficient mechanism of Babaioff et al. (2021) is group strategy-proof for finding EF1 allocations, under matroid-rank valuations. The group strategy-proofness guarantee strengthens the result of Babaioff et al. (2021), that establishes truthfulness (individually for each agent) in the same context. Our result also generalizes a work of Halpern et al. (2020), from binary additive valuations to the matroid-rank case. Next, we establish that an analogous positive result cannot be achieved for MMS, even when considering truthfulness on an individual level. Specifically, we prove that, for matroid-rank valuations, there does not exist a truthful mechanism that is index oblivious, Pareto efficient, and maximin fair. For establishing our results, we develop a characterization of truthful mechanisms for matroid-rank functions. This characterization in fact holds for a broader class of valuations (specifically, holds for binary XOS functions) and might be of independent interest.

poster session 1 @ blue 6, poster session 12 @ blue 6, oral session 1 @ blue 6, poster session 1, poster session 12, oral session 1

We study fair and efficient allocation of divisible goods, in an online manner, among n agents. The goods arrive online in a sequence of T time periods. The agents' values for a good are revealed only after its arrival, and the online algorithm needs to fractionally allocate the good, immediately and irrevocably, among the agents. Towards a unifying treatment of fairness and economic efficiency objectives, we develop an algorithmic framework for finding online allocations to maximize the generalized mean of the values received by the agents. In particular, working with the assumption that each agent's value for the grand bundle of goods is appropriately scaled, we address online maximization of p-mean welfare. Parameterized by an exponent term p in (-infinity, 1], these means encapsulate a range of welfare functions, including social welfare (p=1), egalitarian welfare (p to -infinity), and Nash social welfare (p to 0). We present a simple algorithmic template that takes a threshold as input and, with judicious choices for this threshold, leads to both universal and tailored competitive guarantees. First, we show that one can compute online a single allocation that O (n^{1/2} log n)-approximates the optimal p-mean welfare for all p<=1. The existence of such a universal allocation is interesting in and of itself. Moreover, this universal guarantee achieves essentially tight competitive ratios for specific values of p. Next, we obtain improved competitive ratios for different ranges of p by executing our algorithm with p-specific thresholds, e.g., we provide O(log^3 n)-competitive ratio for all p in (-1/log 2n, 1). We complement our positive results by establishing lower bounds to show that our guarantees are essentially tight for a wide range of the exponent parameter.

poster session 1 @ blue 6, poster session 12 @ blue 6, oral session 1 @ blue 6, poster session 1, poster session 12, oral session 1