Studying evolutionary and coevolutionary games can be seen as an attempt to address a long-standing and fundamental problem in Darwinian evolution. How can the two seemingly contradictory observations be reconciled that individuals experience selective pressure which entails competition in order to be successful in survival and reproduction, but at the same time there is wide-spread cooperative and even altruistic behavior between individuals (and also groups of individuals or even species)? In other words, how can we have selection that favors fitter individuals over less fit, while the same individuals regularly cooperate with and support each other, thus ostensibly leveling off differences in fitness?

Co-evolutionary games may offer answers to these questions as they set up mathematical models to discuss whether, when and under what circumstances cooperation may be more advantageous than competition. Such games define individuals having behavioral choices to be players selecting and executing strategies (for instance cooperation or competition). By linking the relative costs and benefits of strategies to payoff (and subsequently fitness), we obtain a measure of how profitable a given choice is in evolutionary terms. Co-evolutionary games become dynamic if they are played iteratively over several rounds and the players may update their strategies and/or their networks of interaction, which describe with whom a given player interacts in the game. In this context it is common to call games where the players update exclusively their strategies evolutionary games, while games where the players may additionally update their interaction networks are called coevolutionary games.

The tutorial gives an overview about concepts and research questions as well as addressing recent developments in studying co-evolutionary games. Particularly it covers the following topics.

Concepts and mathematical models of evolutionary and coevolutionary games

• Players and strategies o Evolutionary graph theory
• Nash equilibria and evolutionary stable strategies (ESS)
• Strategies and configurations

Games and co-evolutionary dynamics

• Parameterization of the payoff matrix
• Social dilemma games: prisoner's dilemma, snowdrift, stag-hunt, harmony games
• Dilemma strength and universal scaling
• Frequency dependence
• Fixation properties: fixation probabilities and fixation times
• Computational issues
• Replicator dynamics
• Models for updating strategies and interaction networks
• Landscape view on coevolutionary games
• Open questions and research topics

PDF Concepts and recent results in coevolutionary games ↗