Evolutionary game dynamics

By Josef Hofbauer, Karl Sigmund. 2011

1,267 citations recorded by the source corpus.

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.

Subfields: Genetics, Management Science and Operations Research, Sociology and Political Science

View Paper: https://www.semanticscholar.org/paper/eaa839fc0e784f2161d99f231ee2edebd0a2c437

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Citations in the corpus

Individual and cultural learning in stag hunt games with multiple actions (2010, methodology): “We model individual learning using a simple best response learning rule (Gilboa and Matsui, 1991; Hofbauer and Sigmund, 2003).”
Networks beyond pairwise interactions: structure and dynamics (2020, background): “Notice that the competition process can be seen as a game [671, 672], and the right hand side of the equation can be rewritten in the form of a replicator equation for a zero-sum, symmetric matrix game with two players, where the payoffs pij are the entries of the skew-symmetric payoff matrix P =H −”
Options as responses: Grounding behavioural hierarchies in multi-agent RL (2019, methodology): “The rewards accruing to each player are calculated according to the standard anti-symmetric matrix formulation of rock-paper-scissors (as in, e.g., [13]) — r 0 = v 0 M ( v 1 ) T , where v 0 and v 1 are the respective inventories and M is the anti-symmetric matrix of the game.”
Global classification of the planar Lotka–Volterra differential systems according to their configurations of invariant straight lines (2010, background): “There is a large amount of work on Lotka-Volterra differential systems of order n with n ≥ 2 and several monographs contain material on planar or higher order Lotka-Volterra systems for example [42], [41], [55], [58], [56], [32].”
Games on graphs (2014, background): “Evolutionary game theory [54], [53], [17], [89], [118], [37], [38], [66], [12] is the study of evolution when selection depends on the relative abundance (D frequency) of strategies or phenotypes in the population.”
Pursuit and an evolutionary game (2009, background): “(The cost function (2.4) for motion camouflage was introduced in Justh & Krishnaprasad (2006)).”
A Counter-example to Karlin's Strong Conjecture for Fictitious Play (2014, neutral): “Surveys can be found in [ 24], [14], [20].”
The replicator equation and other game dynamics (2014, neutral): “either π1ðp*; p; qÞ> π1ðp; p; qÞ or π2ðq*; p; qÞ> π2ðq; p; qÞ [9]”
Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics (2009, background): “When we restrict ourselves to symmetric games, one can say simply, by an abuse of language [21], that a strategy si is a Nash equilibrium if it is a best reply to itself: Wii Wij , ∀sj (a strict Nash equilibrium if the inequality is strict).”
Nash-type equilibria on Riemannian manifolds: a variational approach (2016, background): “However, it seems that some ideas of the present paper can be efficiently applied to evolutionary game dynamics on curved spaces, see Bomze [5], and Hofbauer and Sigmund [17].”