VirtualLabs in evolutionary game theory
by Christoph Hauert, Version 3.0, February 2005.
October 5th, 2005: Restructuring and extension of the Introduction, and the tutorials on Voluntary participation in Public Goods Games (new sections on oscillations and synchronization and phase transitions added) as well as on traditional Public Goods Games (major extensions of the section on phase transitions). Plus numerous minor fixes.
Quick introduction covering the basic ideas of evolutionary game theory illustrated with many examples. This section briefly introduces classic games such as the Prisoner's Dilemma, the Hawk-Dove- or Snowdrift game and the Rock-Scissors-Paper game. It is intended as an overview of the many features and capabilities of the interactive virtual labs.
Tutorial on the gradual evolution of distinct cooperative and defective behavioral patterns through evolutionary branching into separate trait groups characterized by high and low cooperative investments. This is based on a model that extends the classical Snowdrift game to continuously varying degrees of cooperation. Apart from evolutionary branching, this model exhibits rich dynamics that can be easily explored using this interactive tutorial.
Doebeli, M., Hauert, C. & Killingback, T. (2004) Science 306, 859-862.
Tutorial on the fixation probability of mutants in structured populations where individuals are arranged on a graph. Each node represents an individual that is connected to other individuals. For a large class of graphs, the fixation probability does not depend on the details of the population structure and is identical to a homogenous population. All these graphs display the same characteristic balance between evolutionary selection and random drift. Nevertheless, the structure of the graph can have significant effects on the fixation probability ranging from complete suppression of selection to guaranteed fixation of advantageous mutants.
Lieberman, E., Hauert, C. & Nowak, M. (2005) Nature 433, 312-316.
Tutorial on the fate of cooperative behavior in two closely related evolutionary games: the Prisoner's Dilemma and the Snowdrift (Hawk-Dove) game. The population structure then determines whether the evolution and maintenance of cooperation is promoted or hindered. In particular, this interactive tutorial illustrates that, in contrast to the Prisoner's Dilemma, spatial structure can be detrimental to cooperation in the Snowdrift game.
Hauert, C. & Doebeli, M. (2004) Nature 428, 643-646.
Tutorial on voluntary participation in Public Goods games. Most theoretical and experimental work on social dilemmas has tacitly built on the fact that the interacting individuals are caught in the dilemma. In most real-life situations, however, individuals do have considerable freedom to choose their partners. Whenever a public enterprise appears to risky, individuals may choose to opt out. The rock-sissors-paper type dominance of cooperators, defectors and loners (those that do not participate) often leads to stable co-existence of all three strategies. In spatial settings the cyclic dominance acts as the driving force for traveling waves and other fascinating spatio-temporal patterns.
Hauert, C., De Monte, S., Hofbauer, J. & Sigmund, K. (2002) Science 296 1129-1132.
Tutorial on effects of reward, punishment and reputation in Public Goods games. Various experimental studies on social dilemmas have shown that punishment is very efficient in creating incentives for cooperative behavior. Reward, however, is considerably less efficient. The underlying mechanisms are illustrated with a simple game theoretical model.
Sigmund, K., Hauert, C. & Nowak, M. (2001) Proc. Natl Acad. Sci. USA 98, 10757-10762.
Tutorial on 2×2 games in populations with different structures. 2×2 games describe a rich set of pairwise interactions among individuals. The most prominent game is certainly the Prisoner's Dilemma which has become the paradigm to discuss the emergence of cooperative behavior. If players are arranged on regular lattices, many of these games produce fascinating spatio-temporal patterns. This tutorial provides a hands-on experience of this dynamical world.
Hauert, C. (2002) Int. J. of Bifurcation & Chaos 12 1531-1548.
Tutorial on public goods games in populations with different structures. Public goods games essentially represent a generalization of the pairwise interactions in the Prisoner's Dilemma to groups of arbitrary size. In spatial extended populations where individuals interact only within a limited local neighborhood cooperators can persist through cluster formation. Variations of the value of the public good result in a critical phase transition which relates to percolation phenomena from condensed matter physics.
Szabó, G. & Hauert, C. (2002) Phys. Rev. Lett. 89 (11) 118101.