Users in a social network are usually confronted with decision-making under uncertain network states. While there are some works in the social learning literature on how to construct belief in an uncertain network state, few studies have focused on integrating learning with decision-making for the scenario in which users are uncertain about the network state and their decisions influence each other. Moreover, the population in a social network can be dynamic since users may arrive at or leave the network at any time, which makes the problem even more challenging. In this chapter, we introduce a dynamic Chinese restaurant game to study how a user in a dynamic social network learns about the uncertain network state and makes optimal decisions by taking into account not only the immediate utility, but also subsequent users’ influence. We introduce a Bayesian learning-based method for users to learn the network state and discuss a multidimensional Markov decision process-based approach for users to make optimal decisions. Finally, we apply the dynamic Chinese restaurant game to cognitive radio networks and use simulations to verify the effectiveness of the scheme.

In the third part of this book, the third branch of modern game theory – sequential decision-making – is presented. The important components in sequential decision-making, such as network externality, information asymmetry, and user rationality, are presented and defined. The limitations of the existing approaches, such as social learning and multiarm bandit problems, are also presented.

Network service acquisition in a wireless environment requires the selection of a wireless access network. A key problem in wireless access network selection is studying rational strategies that consider negative network externality. In this chapter, we formulate the wireless network selection problem as a stochastic game with negative network externality and show that finding the optimal decision rule can be modeled as a multidimensional Markov decision process. A modified value-iteration algorithm is utilized to efficiently obtain the optimal decision rule with a simple threshold structure. We further investigate the mechanism design problem with incentive compatibility constraints, which force the networks to reveal truthful state information. The formulated problem is a mixed-integer programming problem that, in general, lacks an efficient solution. Exploiting the optimality of substructures, we introduce a dynamic programming algorithm that can optimally solve the problem in the two-network scenario. For the multinetwork scenario, the dynamic programming algorithm can outperform the heuristic greedy approach in polynomial-time complexity.

In a social network, agents are intelligent and have the capacity to make decisions so as to maximize their utility. They can either make wise decisions by taking advantages of other agents’ experiences through learning or make decisions earlier to avoid competition from huge crowds. Both of these effects – social learning and negative network externality – play important roles in the decision-making process of an agent. In this chapter, a new game called the Chinese restaurant game is introduced to formulate the social learning problem with negative network externality. Through analyzing the Chinese restaurant game, we derive the optimal strategy of each agent and provide a recursive method to achieve the optimal strategy. How social learning and negative network externality influence each other under various settings is studied through simulations. We also illustrate the spectrum access problem in cognitive radio networks as one application of the Chinese restaurant game. We find that the Chinese restaurant game-theoretic approach indeed helps users make better decisions and improves overall system performance.

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.

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.

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.