This chapter covers selected topics in behavioral game theory. We begin with the winner’s curse in common value auctions where players overbid in auctions and make losses. We then consider standard bargaining models such as the Nash bargaining outcome and alternating offers bargaining; the evidence does not support the latter. We introduce evolutionary game theory and the main equilibrium concept, evolutionary stable strategies (ESS). This is followed by a description of replicator dynamics that gives rise to ESS, and a study of its properties. A range of examples illustrate the underlying concepts. We then consider stochastic dynamics generated by an underlying source of persistent randomness and introduce a stochastically stable steady state. Finally, we consider psychological game theory in which beliefs directly enter the utility function allowing for a rigorous modelling of emotions such as guilt and shame.

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.