ABSTRACT
This chapter surveys and investigates the evolutionary dynamics of multiple agents playing strategic games, in the sense of Game Theory (GT), in discrete and continuous strategy spaces. We take the biological perspective towards GT, i.e, known as Evolutionary Game Theory (EGT), to analyze repeated interactions, without perfect information, in multi-agent settings. More precisely, by the application of GT to biology, John Maynard-Smith invented EGT and relaxed the premises behind traditional GT. Classical GT is a normative theory, in the sense that it expects players or agents to be perfectly rational and behave accordingly [von Neumann and Morgenstern, 1944; Weibull, 1996; Redondo, 2003]. In classical GT, interactions between rational agents are modeled as games of two or more players that can choose from a set of strategies and the corresponding preferences. GT is thus the mathematical study of interactive decision making in the sense that the agents involved in the decisions take into account their own choices and those of others. Choices are determined
by stable preferences concerning the outcomes of their possible decisions, and strategic interaction whereby agents take into account the relation between their own choices and the decisions of other agents. Players in the classical setting have a perfect knowledge of the environment and the payoff tables, and try to maximize their individual payoff. However, under the biological circumstances considered by Maynard-Smith, it becomes impossible to judge what choices are the most rational. Instead of figuring out, a priori, how to optimize its actions, the question now facing a player becomes how to learn to optimize its behavior and maximize its return, and it does this based on local knowledge and through a process of trial and error. This learning process matches the concept of evolution in biology, and forms the basis of EGT. In contrast to classical GT, then, EGT is a descriptive theory, describing this process of learning, and does not need the assumption of complete knowledge and perfect rationality.
