Evolutionary Games

Since the workshop held at BIRS in 2006 on the same topic, evolutionary game theory has continued to expand in the directions identified there as well as in several new directions. There seems to be a tendency to reach out from the founding concept of an evolutionarily stable strategy, towards related concepts such as continuously stable strategies and stochastically stable strategies, towards the analysis of polymorphic equilibria and complex population structures, towards a dynamic underpinning of the evolutionary process based on different transmission mechanisms, towards the investigation of how individual information and ongoing interactions impact population behavior, towards a reinterpretation of existing models of population dynamics using a game-theoretic perspective. These directions lead to a large variety of stochastic processes and deterministic dynamics whose interrelation is far from being fully understood. The 2010 workshop aimed to bring together people with different modeling approaches and to allow them to appraise the state of the art in the neighboring fields. This seems all the more useful as evolutionary games have been approached within several different disciplines with very different traditions and also different channels of communication (journals, conferences etc). We mention here classical, economy-based game theory versus biology-driven evolutionary models; probabilistic reasoning based on finite population models versus ordinary differential equations assuming infinite, well mixed populations; equilibrium concepts versus complex attractors; long-term versus short-term evolution; frequency-dependent population genetics versus learning models based on imitation, or endogenous aspiration levels, etc. To give some specific examples, extensive-form games have for decades been analyzed entirely by static classical game theory techniques based on rationality assumptions, but have recently been exhaustively studied from a dynamic perspective in a monograph [8] on evolutionary games and applied to existing models such as signaling games[19]. Classical stochastic processes used in genetics, as for instance the Moran process, have provided the basis for an entirely new analysis of evolutionary dynamics in games in finite populations[15, 23], using concepts such as substitution and fixation. There are surprising relations between different types of deterministic game dynamics, as for instance between the orbits of the best-reply dynamics and the time-averages of solutions of the replicator equation[18]. Non-linear payoff functions are increasingly well understood, for instance through adaptive dynamics[20]; population games have been investigated in depth[28]; games with continuous strategy spaces become increasingly important, and often lead to other predictions than in the discrete case[17]; games on graphs [22, 25] and dynamic graphs [14, 26] are of obvious importance for the evolution of cooperation. The phase-transitions in spatial games attract more and more investigators wielding the tool-box of statistical mechanics and power laws[31], etc.