Stochastic evolutionary game dynamics

1.1 Game theory and evolution Modern game theory goes back to a series of papers by the mathematician John von Neumann in the 1920s. This program started a completely new branch of social sciences and applied mathematics. This early work on game theory is summarized in the seminal book " The Theory of Games and Economic Behavior " by John von Neumann and Oskar Morgenstern [115]. Initially , game theory was primarily focused on cooperative game theory, which analyzes optimal strategies assuming that individuals stick to previous agreements. In the 1950's, the focus shifted to non-cooperative games in which individuals act selfish to get the most out of an interaction. At that time, game theory had matured from a theoretical concept to a scientific field influencing political decision making, mainly in the context of the arms race of the cold war. The basic assumption was that individuals act rationally and take into account that their interaction partners know that their decisions are rational and vice versa. Based on a common utility function that individuals maximize, the actions of others can be predicted and the optimal strategy can be chosen. However, the underlying assumption of rationality is often unrealistic. Even in simple interactions between two individuals A and B, it is difficult to imagine fully rational decision making, as this often leads to an infinite iteration: A thinks of B, who is thinking of A, who is thinking of B and so on. One way to avoid this situation in economy is the idea of bounded rational-ity [32, 91]. If the cost of acquiring and processing information is taken into account, individuals can no longer be assumed to do a fully rational analysis