Network slicing is a critical component in 5G, where each slice can be customized for a given type of service, and a given tenant characterized by a stochastic demand and a resource utility function reflecting its Quality of Service requirements. Considering the slice market as a Stackelberg game, the operator, as the leader, presents pricing for each demand interval and slice type, and the tenants, as followers, decide which demand interval to request. The operator jointly determines the pricing and admission that maximize its revenue while satisfying its capacity constraint. We show NP-hardness of this problem, and a paradox that the operator’s revenue could decrease if a tenant’s resource utility increases. We consider a practical scenario where the tenants’ resource utilities are not known to the operator. For learning an optimal pricing, we propose online approaches based on iteratively updating the operator’s knowledge regarding the resource utilities post its interactions with the tenants, and an offline approach based on neural networks. We study these with respect to various metrics: achieved revenue, reliability, and learning rate. One of our approaches consistently achieves near-optimal revenue irrespective of the number of tenants, with over 95% of optimal revenue within 20 interactions on average.

We study meritocratic fairness in budgeted combinatorial multi-armed bandits with full-bandit feedback, where a learner selects at most K arms per time step and observes only the noisy aggregate reward of the selected set. To define merit under budgeted coalition constraints, we introduce the K-Shapley value, an adaptation of the classical Shapley value that measures marginal contributions using only coalitions of size at most K. We show that the K-Shapley value is the unique solution concept satisfying symmetry, linearity, null player, and K-efficiency axioms. We then establish an Ω(T^2/3) lower bound on fairness regret for monotone submodular valuation functions. We show that an explore-then-commit algorithm MURaS (Meritocratic Uniform Random Sampling) achieves Õ(T^2/3) fairness regret by exploring all arms uniformly in exploration phase. To improve empirical regret, we propose IW-KSVFair, a meritocratic full-bandit algorithm that learns a selection policy whose arm marginals are proportional to the unknown K-Shapley values. To correct the bias induced by adaptive sampling, IW-KSVFair uses importance-weighted estimation and mixes the adaptive set distribution with a uniform distribution to keep importance weights bounded. We prove that IW-KSVFair achieves Õ(T^2/3) fairness regret, matching the lower bound up to logarithmic factors. Experiments on synthetic and real-world datasets show that IW-KSVFair achieves low cumulative fairness regret and closely aligns empirical selection frequencies with K-Shapley value-based merit.

This paper explores the problem of fair assignment of disjoint paths to agents on multi-stage graphs. We motivate the problem by demonstrating that an assignment minimizing the overall cost of all the agents' paths may lead to significant envy among the agents. Showing NP-hardness of finding an envy-minimizing assignment, we propose algorithms that achieve a desired degree of envy while also providing a bound on the Cost of Fairness. Our algorithms run several orders of magnitude faster than a suitably formulated ILP.

This paper explores the problem of fair assignment on Multi-Stage graphs. A multi-stage graph consists of nodes partitioned into K disjoint sets (stages) structured as a sequence of weighted bipartite graphs formed across adjacent stages. The goal is to assign node-disjoint paths to n agents starting from the first stage and ending in the last stage. We show that an efficient assignment that minimizes the overall sum of costs of all the agents' paths may be highly unfair and lead to significant cost disparities (envy) among the agents. We further show that finding an envy-minimizing assignment on a multi-stage graph is NP-hard. We propose the C-Balance algorithm, which guarantees envy that is bounded by 2M in the case of two agents, where M is the maximum edge weight. We demonstrate the algorithm's tightness by presenting an instance where the envy is 2M. We further show that the cost of fairness (CoF), defined as the ratio of the cost of the assignment given by the fair algorithm to that of the minimum cost assignment, is bounded by 2 for C-Balance. We then extend this approach to n agents by proposing the DC-Balance algorithm that makes iterative calls to C-Balance. We show the convergence of DC-Balance, resulting in envy that is arbitrarily close to 2M. We derive CoF bounds for DC-Balance and provide insights about its dependency on the instance-specific parameters and the desired degree of envy. We experimentally show that our algorithm runs several orders of magnitude faster than a suitably formulated ILP.

The literature on investment strategies for steering opinion dynamics on networks primarily focuses on discrete time models. This work proposes an investment framework for a continuous time model that captures essential factors, such as opinion bias, network effect, and camp investment, by extending Friedkin-Johnsen and Taylor's models. We, hence, devise an optimal investment strategy in the presence of various constraints and present its properties, such as memorylessness. We also show that there is a certain adaptability benefit even in the asymptotic regime. When the network structure and the values of the model parameters are not known, we study the learning aspect in two scenarios: first, when opinions of all the nodes are observable, and second, when opinions of a sample set of nodes are observable. We conclude with a simulation study on representative real-world networks and present insights. When all the nodes' opinions are observable, we show that our learning algorithm deduces the exact optimal strategy in very few intervals. When opinions of a sample set of nodes are observable, our learning algorithm is highly accurate and robust for a large enough sample size.

Existing approaches to fairness in stochastic multi-armed bandits (MAB) primarily focus on exposure guarantee to individual arms. When arms are naturally grouped by certain attribute(s), we propose Bi-Level Fairness, which considers two levels of fairness. At the first level, Bi-Level Fairness guarantees a certain minimum exposure to each group. To address the unbalanced allocation of pulls to individual arms within a group, we consider meritocratic fairness at the second level, which ensures that each arm is pulled according to its merit within the group. Our work shows that we can adapt a UCB-based algorithm to achieve a Bi-Level Fairness by providing (i) anytime Group Exposure Fairness guarantees and (ii) ensuring individual-level Meritocratic Fairness within each group. We first show that one can decompose regret bounds into two components: (a) regret due to anytime group exposure fairness and (b) regret due to meritocratic fairness within each group. Our proposed algorithm BF-UCB balances these two regrets optimally to achieve the upper bound of O(√(T)) on regret; T being the stopping time. With the help of simulated experiments, we further show that BF-UCB achieves sub-linear regret; provides better group and individual exposure guarantees compared to existing algorithms; and does not result in a significant drop in reward with respect to UCB algorithm, which does not impose any fairness constraint.

We consider a distributed computing setting wherein a central entity seeks power from computational providers by offering a certain reward in return. The computational providers are classified into long-term stakeholders that invest a constant amount of power over time and players that can strategize on their computational investment. In this paper, we model and analyze a stochastic game in such a distributed computing setting, wherein players arrive and depart over time. While our model is formulated with a focus on volunteer computing, it equally applies to certain other distributed computing applications such as mining in blockchain. We prove that, in Markov perfect equilibrium, only players with cost parameters in a relatively low range which collectively satisfy a certain constraint in a given state, invest. We infer that players need not have knowledge about the system state and other players' parameters, if the total power that is being received by the central entity is communicated to the players as part of the system's protocol. If players are homogeneous and the system consists of a reasonably large number of players, we observe that the total power received by the central entity is proportional to the offered reward and does not vary significantly despite the players' arrivals and departures, thus resulting in a robust and reliable system. We then study by way of simulations and mean field approximation, how the players' utilities are influenced by their arrival and departure rates as well as the system parameters such as the reward's amount and dispensing rate. We observe that the players' expected utilities are maximized when their arrival and departure rates are such that the average number of players present in the system is typically between 1 and 2, since this leads to the system being in the condition of least competition with high probability. Further, their expected utilities increase almost linearly with the offered reward and converge to a constant value with respect to its dispensing rate. We conclude by studying a Stackelberg game, where the central entity decides the amount of reward to offer, and the computational providers decide how much power to invest based on the offered reward.

A synthetic population is a simplified microscopic representation of an actual population. Statistically representative at the population level, it provides valuable inputs to simulation models (especially agent-based models) in research areas such as transportation, land use, economics, and epidemiology. This article describes the datasets from the Synthetic Sweden Mobility (SySMo) model using the state-of-art methodology, including machine learning (ML), iterative proportional fitting (IPF), and probabilistic sampling. The model provides a synthetic replica of over 10 million Swedish individuals (i.e., agents), their household characteristics, and activity-travel plans. This paper briefly explains the methodology for the three datasets: Person, Households, and Activity-travel patterns. Each agent contains socio-demographic attributes, such as age, gender, civil status, residential zone, personal income, car ownership, employment, etc. Each agent also has a household and corresponding attributes such as household size, number of children ≤ 6 years old, etc. These characteristics are the basis for the agents’ daily activity-travel schedule, including type of activity, start-end time, duration, sequence, the location of each activity, and the travel mode between activities.

Battery electric vehicles (BEVs) are vital in the sustainable future of transport systems. Increased BEV adoption makes the realistic assessment of charging infrastructure demand critical. The current literature on charging infrastructure often uses outdated charging behavior assumptions such as universal access to home chargers and the “Liquid-fuel” mental model. We simulate charging infrastructure needs using a large-scale agent-based simulation of Sweden with detailed individual characteristics, including dwelling types and activity patterns. The two state-of-art archetypes of charging behaviors, “Plan-ahead” and “Event-triggered”, mirror the current infrastructure built-up, suggesting 2.3–4.5 times more public chargers per BEV than the “Liquid-fuel” mental model. We also estimate roughly 30–150 BEVs served by a slow charger may be needed for non-home residential overnight charging.

We study fairness in the context of feature-based price discrimination in monopoly markets. We propose a new notion of individual fairness, namely, \alpha-fairness, which guarantees that individuals with similar features face similar prices. First, we study discrete valuation space and give an analytical solution for optimal fair feature-based pricing. We show that the cost of fair pricing is defined as the ratio of expected revenue in an optimal feature-based pricing to the expected revenue in an optimal fair feature-based pricing (CoF) can be arbitrarily large in general. When the revenue function is continuous and concave with respect to the prices, we show that one can achieve CoF strictly less than 2, irrespective of the model parameters. Finally, we provide an algorithm to compute fair feature-based pricing strategy that achieves this CoF.

We study a stochastic game with a dynamic set of players, for modeling and analyzing their computational investment strategies in distributed computing. Players obtain a certain reward for solving a problem, while incurring a certain cost based on the invested time and computational power. We present our framework while considering a contemporary application of blockchain mining, and show that the framework is applicable to certain other distributed computing settings as well. For an in-depth analysis, we consider a particular yet natural scenario where the rate of solving the problem is proportional to the total computational power invested by the players. We show that, in Markov perfect equilibrium, players with cost parameters exceeding a certain threshold, do not invest; while those with cost parameters less than this threshold, invest maximal power. We arrive at an interesting conclusion that the players need not have information about the system state as well as each others' parameters, namely, cost parameters and arrival/departure rates. With extensive simulations and insights through mean field approximation, we study the effects of players' arrival/departure rates and the system parameters on the players' utilities.

In this paper, we introduce ballooning multi-armed bandits (BL-MAB), a novel extension of the classical stochastic MAB model. In the BL-MAB model, the set of available arms grows (or balloons) over time. In contrast to the classical MAB setting where the regret is computed with respect to the best arm overall, the regret in a BL-MAB setting is computed with respect to the best available arm at each time. We first observe that the existing stochastic MAB algorithms result in linear regret for the BL-MAB model. We prove that, if the best arm is equally likely to arrive at any time instant, a sub-linear regret cannot be achieved. Next, we show that if the best arm is more likely to arrive in the early rounds, one can achieve sub-linear regret. Our proposed algorithm determines (1) the fraction of the time horizon for which the newly arriving arms should be explored and (2) the sequence of arm pulls in the exploitation phase from among the explored arms. Making reasonable assumptions on the arrival distribution of the best arm in terms of the thinness of the distribution's tail, we prove that the proposed algorithm achieves sub-linear instance-independent regret. We further quantify explicit dependence of regret on the arrival distribution parameters. We reinforce our theoretical findings with extensive simulation results. We conclude by showing that our algorithm would achieve sub-linear regret even if (a) the distributional parameters are not exactly known, but are obtained using a reasonable learning mechanism or (b) the best arm is not more likely to arrive early, but a large fraction of arms is likely to arrive relatively early.

We model the competition over mining resources and over several cryptocurrencies as a non-cooperative game. Leveraging results about congestion games, we establish conditions for the existence of pure Nash equilibria and provide efficient algorithms for finding such equilibria. We account for multiple system models, varying according to the way that mining resources are allocated and shared and according to the granularity at which mining puzzle complexity is adjusted. When constraints on resources are included, the resulting game is a constrained resource allocation game for which we characterize a normalized Nash equilibrium. Under the proposed models, we provide structural properties of the corresponding types of equilibrium, e.g., establishing conditions under which at most two mining infrastructures will be active or under which no miners will have incentives to mine a given cryptocurrency.

We propose a setting for two-phase opinion dynamics in social networks, where a node’s final opinion in the first phase acts as its initial biased opinion in the second phase. In this setting, we study the problem of two camps aiming to maximize adoption of their respective opinions, by strategically investing on nodes in the two phases. A node’s initial opinion in the second phase naturally plays a key role in determining the final opinion of that node, and hence also of other nodes in the network due to its influence on them. However, more importantly, this bias also determines the effectiveness of a camp’s investment on that node in the second phase. In order to formalize this two-phase investment setting, we propose an extension of Friedkin–Johnsen model, and hence formulate the utility functions of the camps. We arrive at a decision parameter which can be interpreted as two-phase Katz centrality. There is a natural tradeoff while splitting the available budget between the two phases. A lower investment in the first phase results in worse initial biases in the network for the second phase. On the other hand, a higher investment in the first phase spares a lower available budget for the second phase, resulting in an inability to fully harness the influenced biases. We first analyze the non-competitive case where only one camp invests, for which we present a polynomial time algorithm for determining an optimal way to split the camp’s budget between the two phases. We then analyze the case of competing camps, where we show the existence of Nash equilibrium and that it can be computed in polynomial time under reasonable assumptions. We conclude our study with simulations on real-world network datasets, in order to quantify the effects of the initial biases and the weightage attributed by nodes to their initial biases, as well as that of a camp deviating from its equilibrium strategy. Our main conclusion is that, if nodes attribute high weightage to their initial biases, it is advantageous to have a high investment in the first phase, so as to effectively influence the biases to be harnessed in the second phase.

For any company, multiple channels are available for reaching a population in order to market its products. Some of the most well-known channels are (a) mass media advertisement, (b) recommendations using social advertisement, and (c) viral marketing using social networks. The company would want to maximize its reach while also accounting for simultaneous marketing of competing products, where the product marketings may not be independent. In this direction, we propose and analyze a multi-featured generalization of the classical linear threshold model. We hence develop a framework for integrating the considered marketing channels into the social network, and an approach for allocating budget among these channels.

We model the competition over several blockchains characterizing multiple cryptocurrencies as a non-cooperative game. Then, we specialize our results to two instances of the general game, showing properties of the Nash equilibrium. In particular, leveraging results about congestion games, we establish the existence of pure Nash equilibria and provide efficient algorithms for finding such equilibria.

We study the problem of optimally investing in nodes of a social network in a competitive setting, wherein two camps aim to drive the average opinion of the population in their own favor. Using a well-established model of opinion dynamics, we formulate the problem as a zero-sum game with its players being the two camps. We derive optimal investment strategies for both camps, and show that a random investment strategy is optimal when the underlying network follows a popular class of weight distributions. We study a broad framework, where we consider various well-motivated settings of the problem, namely, when the influence of a camp on a node is a concave function of its investment on that node, when a camp aims at maximizing competitors investment or deviation from its desired investment, and when one of the camps has uncertain information about the values of the model parameters. We also study a Stackelberg variant of this game under common coupled constraints on the combined investments by the camps and derive their equilibrium strategies, and hence quantify the first-mover advantage. For a quantitative and illustrative study, we conduct simulations on real-world datasets and provide results and insights.

Given a large population, it is an intensive task to gather individual preferences over a set of alternatives and arrive at an aggregate or collective preference of the population. We show that social network underlying the population can be harnessed to accomplish this task effectively, by sampling preferences of a small subset of representative nodes. We first develop a Facebook app to create a dataset consisting of preferences of nodes and the underlying social network, using which, we develop models that capture how preferences are distributed among nodes in a typical social network. We hence propose an appropriate objective function for the problem of selecting best representative nodes. We devise two algorithms, namely, Greedy-min which provides a performance guarantee for a wide class of popular voting rules, and Greedy-sum which exhibits excellent performance in practice. We compare the performance of these proposed algorithms against random-polling and popular centrality measures, and provide a detailed analysis of the obtained results. Our analysis suggests that selecting representatives using social network information is advantageous for aggregating preferences related to personal topics (e.g., lifestyle), while random polling with a reasonable sample size is good enough for aggregating preferences related to social topics (e.g., government policies).

We study a stochastic game framework with dynamic set of players, for modeling and analyzing their computational investment strategies in distributed computing. Players obtain a certain reward for solving the problem or for providing their computational resources, while incur a certain cost based on the invested time and computational power. We first study a scenario where the reward is offered for solving the problem, such as in blockchain mining. We show that, in Markov perfect equilibrium, players with cost parameters exceeding a certain threshold, do not invest; while those with cost parameters less than this threshold, invest maximal power. Here, players need not know the system state. We then consider a scenario where the reward is offered for contributing to the computational power of a common central entity, such as in volunteer computing. Here, in Markov perfect equilibrium, only players with cost parameters in a relatively low range in a given state, invest. For the case where players are homogeneous, they invest proportionally to the 'reward to cost' ratio. For both the scenarios, we study the effects of players' arrival and departure rates on their utilities using simulations and provide additional insights.

We study the effectiveness of using multiple phases for maximizing the extent of information diffusion through a social network, and present insights while considering various aspects. In particular, we focus on the well-studied independent cascade model with the possibility of adaptively selecting seed nodes in multiple phases based on the observed diffusion in preceding phases, and conduct a detailed simulation study on real-world network datasets. We first present a negative result that more phases do not guarantee a better spread, however the adaptability advantage of using more phases generally leads to a better spread on real-world datasets. We study how diffusing in multiple phases affects the mean and standard deviation of the extent of diffusion, and explain how using multiple phases reduces uncertainty in diffusion. We then study how the number of phases impacts the effectiveness of diffusion, how the diffusion progresses phase-by-phase, and how to optimally split the total seeding budget across phases. Our experiments show a significant gain when we move from single phase to two phases, however, the marginal gain of having an additional phase decreases as we increase the number of phases. Our main conclusion is that, given the number of phases, an optimal way to split the budget across phases is such that the expected number of influenced nodes in each phase is almost the same.