%0 Journal Article %1 Hofbauer2003 %A Hofbauer, Josef %A Sigmund, Karl %D 2003 %J American Mathematical Society %K imported %P 479--519 %T Evolutionary Game Dynamics %U http://ftp.ams.org/bull/2003-40-04/S0273-0979-03-00988-1/S0273-0979-03-00988-1.pdf %V 40 %X Evolutionary game dynamics is the application of population dynamical methods to game theory. It has been introduced by evolutionary biologists, anticipated in part by classical game theorists. In this survey, we present an overview of the many brands of deterministic dynamical systems motivated by evolutionary game theory, including ordinary differential equations (and, in particular, the replicator equation), differential inclusions (the best response dynamics), difference equations (as, for instance, fictitious play) and reaction-diffusion systems. A recurrent theme (the so-called `folk theorem of evolutionary game theory') is the close connection of the dynamical approach with the Nash equilibrium, but we show that a static, equilibrium-based viewpoint is, on principle, unable to always account for the long-term behaviour of players adjusting their behaviour to maximise their payoff.

@article{Hofbauer2003, abstract = {Evolutionary game dynamics is the application of population dynamical methods to game theory. It has been introduced by evolutionary biologists, anticipated in part by classical game theorists. In this survey, we present an overview of the many brands of deterministic dynamical systems motivated by evolutionary game theory, including ordinary differential equations (and, in particular, the replicator equation), differential inclusions (the best response dynamics), difference equations (as, for instance, fictitious play) and reaction-diffusion systems. A recurrent theme (the so-called `folk theorem of evolutionary game theory') is the close connection of the dynamical approach with the Nash equilibrium, but we show that a static, equilibrium-based viewpoint is, on principle, unable to always account for the long-term behaviour of players adjusting their behaviour to maximise their payoff.}, added-at = {2016-12-19T12:09:05.000+0100}, author = {Hofbauer, Josef and Sigmund, Karl}, biburl = {https://www.bibsonomy.org/bibtex/21b45d5233111f8754ac3f133744e43ba/swarmlab}, interhash = {597f98b9d6f61dcee9dfe93a42f998bb}, intrahash = {1b45d5233111f8754ac3f133744e43ba}, journal = {American Mathematical Society}, keywords = {imported}, month = {June}, pages = {479--519}, pdf = {C:\Documents and Settings\G.J.C. van Ahee\Mijn documenten\TU\Mech Design\IN 4027\hofbauer03.pdf}, timestamp = {2016-12-19T12:18:59.000+0100}, title = {{E}volutionary {G}ame {D}ynamics}, url = {http://ftp.ams.org/bull/2003-40-04/S0273-0979-03-00988-1/S0273-0979-03-00988-1.pdf}, volume = 40, year = 2003 }