Xiaohui Bei

Bounded budget betweenness centrality game for strategic network formations

In computer networks and social networks, the betweenness centrality of a node measures the amount of information passing through the node when all pairs are conducting shortest path exchanges. In this paper, we introduce a strategic network formation game in which nodes build connections subject to a budget constraint in order to maximize their betweenness in the network. To reflect real world scenarios where short paths are more important in information exchange in the network, we generalize the betweenness definition to only count shortest paths with a length limit @? in betweenness calculation. We refer to this game as the bounded budget betweenness centrality game and denote it as @?- B^3C game, where @? is the path length constraint parameter. We present both complexity and constructive existence results about Nash equilibria of the game. For the nonuniform version of the game where node budgets, link costs, and pairwise communication weights may vary, we show that Nash equilibria may not exist and it is NP-hard to decide whether Nash equilibria exist in a game instance. For the uniform version of the game where link costs and pairwise communication weights are one and each node can build k links, we construct two families of Nash equilibria based on shift graphs, and study the properties of Nash equilibria. Moreover, we study the complexity of computing best responses and show that the task is polynomial for uniform 2- B^3C games and NP-hard for other games (i.e. uniform @?- B^3C games with @?>=3 and nonuniform @?- B^3C games with @?>=2).

Bounded Budget Betweenness Centrality Game for Strategic Network Formations

In this paper, we introduce the bounded budget betweenness centrality game, a strategic network formation game in which nodes build connections subject to a budget constraint in order to maximize their betweenness centrality, a metric introduced in the social network analysis to measure the information flow through a node. To reflect real world scenarios where short paths are more important in information exchange, we generalize the betweenness definition to only consider shortest paths of length at most `. We present both complexity and constructive existence results about Nash equilibria of the game. For the nonuniform version of the game where node budgets, link costs, and pairwise communication weights may vary, we show that Nash equilibria may not exist and it is NP-hard to decide whether Nash equilibria exist in a game instance. For the uniform version of the game where link costs and pairwise communication weights are one and each node can build k links, we construct two families of Nash equilibria based on shift graphs, and study the properties of Nash equilibria. Moreover, we study the complexity of computing best responses and show that the task is polynomial for uniform 2-BC games and NP-hard for other games.

Solving Linear Programming with Constraints Unknown

What is the value of input information in solving linear programming? The celebrated ellipsoid algorithm tells us that the full information of input constraints is not necessary; the algorithm works as long as there exists an oracle that, on a proposed candidate solution, returns a violation in the form of a separating hyperplane. Can linear programming still be efficiently solved if the returned violation is in other formats?

Cake Cutting: Envy and Truth

We study envy-free cake cutting with strategic agents, where each agent may manipulate his private information in order to receive a better allocation. We focus on piecewise constant utility functions and consider two scenarios: the general setting without any restriction on the allocations and the restricted setting where each agent has to receive a connected piece. We show that no deterministic truthful envy-free mechanism exists in the connected piece scenario, and the same impossibility result for the general setting with some additional mild assumptions on the allocations. Finally, we study a large market model where the economy is replicated and demonstrate that truth-telling converges to a Nash equilibrium.

Networked Fairness in Cake Cutting

We introduce a graphical framework for fair division in cake cutting, where comparisons between agents are limited by an underlying network structure. We generalize the classical fairness notions of envy-freeness and proportionality to this graphical setting. Given a simple undirected graph G, an allocation is envy-free on G if no agent envies any of her neighbors share, and is proportional on G if every agent values her own share no less than the average among her neighbors, with respect to her own measure. These generalizations open new research directions in developing simple and efficient algorithms that can produce fair allocations under specific graph structures. On the algorithmic frontier, we first propose a moving-knife algorithm that outputs an envy-free allocation on trees. The algorithm is significantly simpler than the discrete and bounded envy-free algorithm recently designed by Aziz and Mackenzie for complete graphs. Next, we give a discrete and bounded algorithm for computing a proportional allocation on descendant graphs, a class of graphs by taking a rooted tree and connecting all its ancestor-descendant pairs.

Earning limits in fisher markets with spending-constraint utilities

Earning limits are an interesting novel aspect in the classic Fisher market model. Here sellers have bounds on their income and can decide to lower the supply they bring to the market if income exceeds the limit. Beyond several applications, in which earning limits are natural, equilibria of such markets are a central concept in the allocation of indivisible items to maximize Nash social welfare.

Computing Equilibria in Markets with Budget-Additive Utilities

We present the first analysis of Fisher markets with buyers that have budget-additive utility functions. Budget-additive utilities are elementary concave functions with numerous applications in online adword markets and revenue optimization problems. They extend the standard case of linear utilities and have been studied in a variety of other market models. In contrast to the frequently studied CES utilities, they have a global satiation point which can imply multiple market equilibria with quite different characteristics. Our main result is an efficient combinatorial algorithm to compute a market equilibrium with a Pareto-optimal allocation of goods. It relies on a new descending-price approach and, as a special case, also implies a novel combinatorial algorithm for computing a market equilibrium in linear Fisher markets. We complement this positive result with a number of hardness results for related computational questions. We prove that it isNP-hard to compute a market equilibrium that maximizes social welfare, and it is PPAD-hard to find any market equilibrium with utility functions with separate satiation points for each buyer and each good.

Ascending-Price Algorithms for Unknown Markets

We design a simple ascending-price algorithm to compute a (1+\varepsilon)-approximate equilibrium in Arrow-Debreu exchange markets with weak gross substitute (WGS) property, which runs in time polynomial in market parameters and log 1/varepsilon. This is the first polynomial-time algorithm for most of the known tractable classes of Arrow-Debreu markets, which is easy to implement and avoids heavy machinery such as the ellipsoid method. In addition, our algorithm can be applied in an unknown market setting without exact knowledge about the number of agents, their individual utilities and endowments. Instead, our algorithm only relies on queries to a global demand oracle by posting prices and receiving aggregate demand for goods as feedback. When demands are real-valued functions of prices, the oracles can only return values of bounded precision based on real utility functions. Due to this more realistic assumption, precision and representation of prices and demands become a major technical challenge, and we develop new tools and insights that may be of independent interest. Furthermore, our approach also gives the first polynomial-time algorithm to compute an exact equilibrium for markets with spending constraint utilities, a piecewise linear concave generalization of linear utilities. This resolves an open problem posed by~\citet{DuanM15}.

Trial and error in influential social networks

In this paper, we introduce a trial-and-error model to study information diffusion in a social network. Specifically, in every discrete period, all individuals in the network concurrently try a new technology or product with certain respective probabilities. If it turns out that an individual observes a better utility, he will then adopt the trial; otherwise, the individual continues to choose his prior selection. We first demonstrate that the trial and error behavior of individuals characterizes certain global community structures of a social network, from which we are able to detect macro-communities through the observation of micro-behavior of individuals. We run simulations on classic benchmark testing graphs, and quite surprisingly, the results show that the trial and error dynamics even outperforms the Louvain method (a popular modularity maximization approach) if individuals have dense connections within communities. This gives a solid justification of the model. We then study the influence maximization problem in the trial-and-error dynamics. We give a heuristic algorithm based on community detection and provide experiments on both testing and large scale collaboration networks. Simulation results show that our algorithm significantly outperforms several well-studied heuristics including degree centrality and distance centrality in almost all of the scenarios. Our results reveal the relation between the budget that an advertiser invests and marketing strategies, and indicate that the mixing parameter, a benchmark evaluating network community structures, plays a critical role for information diffusion.

An Efficient Auction with Variable Reserve Prices for Ridesourcing

Ridesourcing refers to the service that matches passengers who need a car to personal drivers. In this work, we study an auction model for ridesourcing that sells multiple items to unit-demand single-parameter agents with variable reserve price constraints. In this model, there is an externally imposed reserve price set for every item, and the price is both item- and bidder-dependent. Such auctions can also find applications in a number of other traditional and online markets, such as ad auction or online laboring market.