Many spectrum sensing methods and dynamic access algorithms have been proposed to improve secondary users’ access opportunities. However, few of them have considered integrating the design of spectrum sensing and access algorithms together by taking into account the mutual influence between them. In this chapter, we focus on jointly analyzing the spectrum sensing and access problem. Due to their selfish nature, secondary users tend to act selfishly to access the channel without contributing to spectrum sensing. Moreover, they may employ out-of-equilibrium strategies because of the uncertainty of others’ strategies. To model the complicated interactions among secondary users, the joint spectrum sensing and access problem is formulated as an evolutionary game and the evolutionarily stable strategy (ESS) that no one will deviate from is studied. Furthermore, a distributed learning algorithm for the secondary users to converge to the ESS is introduced. Simulation results shows that the system can quickly converge to the ESS and such an ESS is robust to the sudden unfavorable deviations of the selfish secondary users.

Cooperation is a promising approach to simultaneously achieving efficient spectrum resource use and improving the quality of service of primary users in dynamic spectrum access networks. However, due to their selfish nature, how to stimulate secondary users to play cooperatively is an important issue. In this chapter, we discuss a reputation-based spectrum access framework where the cooperation stimulation problem is modeled as an indirect reciprocity game. In this game, secondary users choose how to help primary users relay information and gain reputation, based on which they can access a certain amount of vacant licensed channels in the future. By formulating a secondary user's decision-making as a Markov decision process, the optimal action rule can be obtained, according to which the secondary user will use maximal power to help the primary user relay data and thus greatly improve the primary user's quality of service as well as the spectrum utilization efficiency. Moreover, the uniqueness of the stationary reputation distribution is proved, and the conditions under which the optimal action rule is evolutionarily stable are theoretically derived.

The motivation of this book and necessary background knowledge of this book are provided. First, a brief introduction to competition and cooperation in wireless and social networks is provided, along with examples and a literature review. Then, the limitations of traditional game theory in this area are presented. Finally, the three branches of modern game theory – indirect reciprocity, evolutionary games, and sequential decision-making – will be briefly mentioned to illustrate their strengths for overcoming the highlighted limitations.

Deal selection on Groupon represents a typical social learning and decision-making process, where the quality of a deal is usually unknown to the customers. The customers must acquire this knowledge through social learning from other social media, such as reviews on Yelp. Additionally, the quality of a deal depends on both the state of the vendor and the decisions of other customers on Groupon. How social learning and network externality affect the decisions of customers in deal selection on Groupon is the main focus of this chapter. We develop a data-driven game-theoretic framework to understand rational deal selection behaviors across social media. The sufficient condition of the Nash equilibrium is identified. A value-iteration algorithm is utilized to find the optimal deal selection strategy. We utilize the Groupon–Yelp data set to analyze the deal selection game in a realistic setting. Finally, the performance of the social learning framework is evaluated using real data. The results suggest that customers make decisions in a rational way instead of following naive strategies, and there is still room to improve their decisions with assistance from a game-theoretic framework.

How information diffuses over social networks has attracted much attention from both industry and academics. Most of the existing works in this area are based on machine learning methods focusing on social network structure analysis and empirical data mining. However, the network users’ decisions, actions, and socioeconomic interactions are generally ignored in most existing works. In this chapter, we discuss an evolutionary game-theoretic framework to model the dynamic information diffusion process in social networks. Specifically, we derive the information diffusion dynamics in complete networks and uniform-degree and nonuniform-degree networks. We find that the dynamics of information diffusion over these three kinds of networks are scale-free and the same as each other when the network scale is sufficiently large. To verify the theoretical analysis, we perform simulations of the information diffusion over synthetic networks and real-world Facebook networks. Moreover, we conduct an experiment on the Twitter hashtag data set, which shows that the game-theoretic model well fits and predicts information diffusion over real social networks.

Distributed adaptive filtering has been considered to be an effective approach for data processing and estimation over distributed networks. Most existing algorithms focus on designing different information diffusion rules, regardless of the evolutionary characteristics of a distributed network. In this chapter, we study the adaptive network from the game-theoretic perspective and formulate the distributed adaptive filtering problem as a graphical evolutionary game. With this formulation, the nodes in the network are regarded as players and the local combiner of estimated information from different neighbors is regarded as a form of diverse strategy selection. We show that this graphical evolutionary game framework is very general and can unify the existing adaptive network algorithms. Based on this framework, as examples, two error-aware adaptive filtering algorithms are discussed. Moreover, we use graphical evolutionary game theory to analyze the information diffusion process over the adaptive networks and the evolutionarily stable strategy of the system. Finally, simulation results are shown to verify the effectiveness of the method discussed in this chapter.

The effectiveness of a decision may be uncertain due to the unknown system state. This uncertainty can be eliminated through learning from information sources, such as user-generated content or revealed actions. Nevertheless, user-generated content could be untrustworthy, since other agents may maliciously create misleading content for their selfish interests. Passively revealed actions are potentially more trustworthy and also easier to gather through simple observation. In this chapter, we introduce a game-theoretic framework – the hidden Chinese restaurant game (H-CRG) – to utilize the passively revealed actions in social learning process. We design grand information extraction, a novel Bayesian belief extraction process, to extract beliefs on hidden information directly from observed actions. The optimal policy is then analyzed in both centralized and game-theoretic approaches. We demonstrate how the H-CRG can be applied to the channel access problem in cognitive radio networks. The simulation results show that the equilibrium strategy derived in the H-CRG provides greater expected utilities for new users and maintains reasonably high social welfare.

In many social computing systems, users decide sequentially whether to participate or not and, if they participate, whether to create a piece of content directly (i.e. answering) or to rate existing content contributed by previous users (i.e. voting). We present in this chapter a game-theoretic model that formulates the sequential decision-making of strategic users under the presence of this answering–voting externality. We prove theoretically the existence and uniqueness of a pure strategy equilibrium. We show that there exist advantages for users with higher abilities and for answering earlier. Therefore, the equilibrium exhibits a threshold structure and the threshold for answering gradually increases as answers accumulate. To show the validness of the game-theoretic model, we analyze user behavior data collected from a popular question-and-answer site Stack Overflow and show that the main qualitative predictions of the game-theoretic model match up with observations made from the data. Finally, we formulate the system designer’s problem and abstract several design principles that could potentially guide the design of incentive mechanisms for social computing systems in practice.

The basics of game theory, which are necessary for understanding the rest of the book, are provided in this chapter. Specifically, typical game compoments, solution concepts, and their applications are explained.

Users may have multiple concurrent options regarding different objects/resources and their decisions usually negatively influence each other’s utility, which makes the sequential decision-making problem more challenging. In this chapter, we introduce an Indian buffet game to study how users in a dynamic system learn about the uncertain system state and make multiple concurrent decisions by not only considering their current myopic utility, but also the influence of subsequent users’ decisions. We analyze the Indian buffet game under two different scenarios: one of customers requesting multiple dishes without budget constraints and the other with budget constraints. In both cases, we design recursive best-response algorithms to find the subgame-perfect Nash equilibrium for customers and characterize special properties of the Nash equilibrium profile in a homogeneous setting. Moreover, we introduce a non-Bayesian social learning algorithm by which customers can learn the system state, and we theoretically prove its convergence. Finally, we conduct simulations to validate the effectiveness and efficiency of the Indian buffet game.

Data sharing is a critical step in implementing data fusion, and how to encourage sensors to share their data is an important issue. In this chapter, we discuss a reputation-based incentive framework where the data-sharing stimulation problem is modeled as an indirect reciprocity game. In this game, sensors choose how to report their results to the fusion center and gain reputation, based on which they can obtain certain benefits in the future. Taking the sensing and fusion accuracy into account, reputation distribution is introduced into the game, where we prove theoretically the Nash equilibrium of the game and its uniqueness. Furthermore, we apply the scheme to cooperative spectrum sensing. We show that, within an appropriate cost-to-gain ratio, the optimal strategy for the secondary users is to report when the average received energy is above a given threshold and to keep silent otherwise. Such an optimal strategy is also proved to be a desirable evolutionarily stable strategy.

Here we discuss how the use of artificial intelligence will change the way science is done. Deep learning algorithms can now surpass the performance of human experts, a fact that has major implications for the future of our discipline. Successful uses of AI technology all possess two ingredients for deep learning: copious training data and a clear way to classify it. When these two conditions are met, researchers working in tandem with AI technologies can organize information and solve scientific problems with impressive efficiency. The future of science will increasingly rely on human–machine partnerships, where people and computers work together, revolutionizing the scientific process. We provide an example of what this may look like. Hoping to remedy a present-day challenge in science known as the “reproducibility crisis,” researchers used deep learning to uncover patterns in papers that signal strong and weak scientific findings. By combining the insights of machines and humans, the new AI model acheives the highest predictive accuracy.

We begin by discussing the challenges of quantifying scientific impact. We introduce the h-index and explore its implications for scientists. We also detail the h-index’s strengths when compared with other metrics, and show that it bypasses all the disadvantages posed by alternative ranking systems. We then explore the h-index’s predictive power, finding that it provides an easy but relatively accurate estimate of a person’s acheivements. Despite its relative accuracy, we are aware of the h-index’s limitations, which we detail here with suggestions for possible remedies.

To describe coauthorship networks, we begin with the Erdös number, which links mathematicians to their famously prolific colleague through the papers they have collaborated on. Coauthorship networks help us capture collaborative patterns and identify important features that characterize them. We can also use them to predict how many collaborators a scientist will have in the future based on her coauthorship history. We find that collaboration networks are scale-free, following a power-law distribution. As a consequence of the Matthew effect, frequent collaborators are more likely to collaborate, becoming hubs in their networks. We then explore the small-world phenomenon evidenced in coauthorship networks, which is sometimes referred to as “six degrees of separation.” To understand how a network’s small-worldliness impacts creativity and success, we look to teams of artists collaborating on Broadway musicals, finding that teams perform best when the network they inhabit is neither too big or too small. We end by discussing how connected components within networks provide evidence for the “invisible college.”

We introduce the role that productivity plays in scientific success by describing Paul Erdös’ exceptional productivity. How does Erdös’ productivity measure up to other scientists? Is the exponential increase in the number of papers published due to rising productivity rates or to the growing number of scientists working in the discipline? We find that there is an increase in the productivity of individual scientists but that that increase is due to the growth of collaborative work in science. We also quantify the significant productivity differences between disciplines and individual scientists. Why do these differences exist? To answer this question, we explore Shockley’s work on the subject, beginning with his discovery that productivity follows a lognormal distribution. We outline his hurdle model of productivity, which not only explains why the productivity distribution is fat-tailed, but also provides a helpful framework for improving individual scientific output. Finally, we outline how productivity is multiplicative, but salaries are additive, a contradiction that has implications for science policy.

Here we address bias and causality, beginning with the bias against failure in the existing science of science research. Because the data available to us is mostly on published papers, we necessarily disregard the role that failure plays in a scientific career. This could be framed as a surviorship bias, where the “surviving” papers are those that make it to publication. This same issue can be seen as a flaw in our current definition of impact, since our use of citation counts keeps a focus on success in the discipline. We explore the drawbacks and upsides of variants on citation counts, including altmetrics like page views. We also look at how possible ways to expand the science of science to include unobservable factors, as we saw in the case of the credibility revolution in economics. Using randomized controlled trials and natural experiments, the science of science could explore causality more deeply. Given the tension between certainty and generalizability, both experimental and observational insights are important to our understanding of how science works.

While there is plenty of information available about the luminaries of science, here we discuss the relative lack of information about ordinary researchers. Luckily, because of recent advances in name disambiguation, the career histories of everyday scientists can now be analyzed, changing the way we think about scientific creativity entirely. We describe how the process of shuffling a career – moving the works a scientist publishes around randomly in time – helped us discover what we call the “random impact rule,” which dictates that, when we adjust for productivity, the highest impact work in a career can occur at any time. We also see that the probability of landmark work follows a cumulative distribution, meaning that the random impact rule holds true not just for the highest impact work in any career but also for other important works, too. While there is precedent for this rule in the literature – Simonton proposed the “constant probability of success” model in the 1970s – until recently we didn’t have the data on hand to test it. The random impact rule allows us to decouple age and creativity, instead linking periods of high productivity to creative breakthroughs.