Reciprocity is a mechanism for the evolution of cooperation. This mechanism explains cooperation among unrelated individuals by an assortment in which individuals restrict their interaction partners to avoid being exploited by defectors. Three types of reciprocal mechanisms have been proposed: direct reciprocity, indirect reciprocity, and network (spatial) reciprocity. Direct reciprocity is a behavior whereby an individual acts in a manner that temporarily reduces his or her fitness while increasing another individual’s fitness with the expectation that the other individual will behave similarly at a later time. If individuals who use direct reciprocity both regard each other as cooperative, they will establish reciprocal relationships. Indirect reciprocity is a mechanism that enables individuals to establish cooperative relationships, e.g., by evaluating others’ behavior, without having direct interactions, which are required by direct reciprocity. If an individual cooperates with individuals with good reputations and that individual establishes a good reputation, cooperation via indirect reciprocity can occur. Network reciprocity explains reciprocal relationships via restriction of interaction, e.g., network and spatial restrictions, namely, individuals interact with fixed individuals in a network. If cooperative clusters arise, cooperators realize high fitness by cooperating with each other. Theoretical studies have explored the evolutionary stability of the cooperation that facilitates these reciprocities. Experimental studies have examined the evidence for these reciprocities according to the theoretical studies. These theoretical and experimental studies assume a simple interaction among individuals for cooperative and reciprocal behavior, such as in evolutionary game theory. By examining such theoretical and experimental evidence in a less restrictive environment, these pieces of evidence can be generalized to natural environments and real life. Human behavior logs on the Internet, e.g., online games, can be utilized in such studies. In this chapter we review the theory and evidence for the three types of reciprocities. First, we introduce evolutionary game theory as a framework for the evolution of cooperation, such as reciprocal altruism. Second, we explain the three types of reciprocity by reviewing results of theoretical studies. Third, we present experimental evidence for human reciprocity, which supports these evolutionary theories of reciprocity. Finally, we present empirical evidence for human reciprocity in practice using an online game dataset, which represents a less restrictive environment.

In cognitive networks, how to stimulate cooperation among nodes is very important. However, most existing game-theoretic cooperation stimulation approaches rely on the assumption that the interactions between any pair of players are long-lasting. When this assumption is not true, such as in the well-known Prisoner’s dilemma and the backward induction principle, the unique Nash equilibrium is to always play noncooperatively. In this chapter, we discuss a cooperation stimulation scheme for the scenario in which the number of interactions is finite. This scheme is based on indirect reciprocity game modeling where the key concept is “I help you not because you have helped me but because you have helped others.” The problem of finding the optimal action rule is formulated as a Markov decision process, and a modified value-iteration algorithm is utilized to find the optimal action rule. Using the packet forwarding game as an example, it is shown that with an appropriate cost-to-gain ratio, the strategy of forwarding the number of packets that is equal to the reputation level of the receiver is an evolutionarily stable strategy.

The viability of cooperative communications depends on the willingness of users to help. Therefore, it is important to study incentive issues when designing such systems. In this chapter, we discuss a cooperation stimulation scheme for multiuser cooperative communications using an indirect reciprocity game. By introducing the notion of reputation and social norms, rational users who care about their future utility are incentivized to cooperate with others. Differently from existing works on reputation-based schemes that mainly rely on experimental verification, the effectiveness of the scheme is demonstrated in two steps. First, we conduct a steady-state analysis of the game and show that cooperating with users who have a good reputation can be sustained as an equilibrium when the cost-to-gain ratio is below a certain threshold. Then, by modeling the action spreading at transient states as an evolutionary game, we show that the equilibria we found in the steady-state analysis are stable and can be reached with proper initial conditions. Moreover, we introduce energy detection to handle the possible cheating behaviors of users and study its impact on the indirect reciprocity game.

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.

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.

This chapter focusses principally on considering the different forms of reciprocity, driven variously by purported fairness, liking and/or enlightened self-interest. Reciprocity can be direct (i.e. where exchange partners are known to each other), indirect (i.e. where they are not) and negative (i.e. punishment for transgressions), and there is in general a concern both for the intentions of others and for the final distribution of outcomes. Reciprocity can be all of these things because its expression is contextual – the meaning that people attach to the way the context is framed drives behavioural responses, and if care is not taken reciprocity can be crowded out for what many may perceive as our baser instincts. The contextual nature of reciprocity is illustrated in the chapter with reference to a simple economic abstraction known as the ultimatum game. Ultimately, however, in an evolutionary sense perhaps the most fundamental reason for acting reciprocally is that it can bring about benefits and protection to the group, and most people perhaps know innately that what is good for the group is good for them individually, also.