Alexandros A. Voudouris

Welfare Guarantees for Proportional Allocations

According to the proportional allocation mechanism from the network optimization literature, users compete for a divisible resource – such as bandwidth – by submitting bids. The mechanism allocates to each user a fraction of the resource that is proportional to her bid and collects an amount equal to her bid as payment. Since users act as utility-maximizers, this naturally defines a proportional allocation game. Recently, Syrgkanis and Tardos (STOC 2013) quantified the inefficiency of equilibria in this game with respect to the social welfare and presented a lower bound of 26.8% on the price of anarchy over coarse-correlated and Bayes-Nash equilibria in the full and incomplete information settings, respectively. In this paper, we improve this bound to 50% over both equilibrium concepts. Our analysis is simpler and, furthermore, we argue that it cannot be improved by arguments that do not take the equilibrium structure into account. We also extend it to settings with budget constraints where we show the first constant bound (between 36% and 50%) on the price of anarchy of the corresponding game with respect to an effective welfare benchmark that takes budgets into account.

Efficiency and complexity of price competition among single-product vendors ☆

Abstract Motivated by recent progress on pricing in the AI literature, we study marketplaces that contain multiple vendors offering identical or similar products and unit-demand buyers with different valuations on these vendors. The objective of each vendor is to set the price of its product to a fixed value so that its profit is maximized. The profit depends on the vendors price itself and the total volume of buyers that find the particular price more attractive than the price of the vendors competitors. We model the behavior of buyers and vendors as a two-stage full-information game and study a series of questions related to the existence, efficiency (price of anarchy) and computational complexity of equilibria in this game. To overcome situations where equilibria do not exist or exist but are highly inefficient, we consider the scenario where some of the vendors are subsidized in order to keep prices low and buyers highly satisfied.

How Effective Can Simple Ordinal Peer Grading Be

Ordinal peer grading has been proposed as a simple and scalable solution for computing reliable information about student performance in massive open online courses. The idea is to outsource the grading task to the students themselves as follows. After the end of an exam, each student is asked to rank --- in terms of quality --- a bundle of exam papers by fellow students. An aggregation rule will then combine the individual rankings into a global one that contains all students. We define a broad class of simple aggregation rules and present a theoretical framework for assessing their effectiveness. When statistical information about the grading behaviour of students is available, the framework can be used to compute the optimal rule from this class with respect to a series of performance objectives. For example, a natural rule known as Borda is proved to be optimal when students grade correctly. In addition, we present extensive simulations and a field experiment that validate our theory and prove it to be extremely accurate in predicting the performance of aggregation rules even when only rough information about grading behaviour is available.

Bounding the Inefficiency of Compromise

Social networks on the Internet have seen an enormous growth recently and play a crucial role in different aspects of todays life. They have facilitated information dissemination in ways that have been beneficial for their users but they are often used strategically in order to spread information that only serves the objectives of particular users. These properties have inspired a revision of classical opinion formation models from sociology using game-theoretic notions and tools. We follow the same modeling approach, focusing on scenarios where the opinion expressed by each user is a compromise between her internal belief and the opinions of a small number of neighbors among her social acquaintances. We formulate simple games that capture this behavior and quantify the inefficiency of equilibria using the well-known notion of the price of anarchy. Our results indicate that compromise comes at a cost that strongly depends on the neighborhood size.

Peer-to-Peer Energy-Aware Tree Network Formation

We study the fundamental problem of distributed energy-aware network formation with mobile agents of limited computational power that have the capability to wirelessly transmit and receive energy in a peer-to-peer manner. Specifically, we design simple distributed protocols consisting of a small number of states and interaction rules for the construction of both arbitrary and binary trees. Further, we theoretically and experimentally evaluate a plethora of energy redistribution protocols that exploit different levels of knowledge in order to achieve desired energy distributions which require, for instance, that every agent has twice the energy of the agents of higher depth (according to the tree network). Our study shows that without using any knowledge about the network structure, such energy distributions cannot be achieved in a timely manner, which means that there might be high energy loss during the redistribution process. On the other hand, only a few extra bits of information seem to be enough to guarantee quick convergence to energy distributions that satisfy particular properties, yielding low energy loss.