An Introduction to Evolutionary Game Theory: Lecture 2 - School of ...

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OutlineThe goal of this lecture is to give some insight into the followingtopics:Some Properties of the Replicator DynamicsReplicator Equations for 2 × 2 GamesMoran Process & Evolutionary DynamicsThe Concept of Fixation ProbabilityEvolutionary Game Theory in Finite PopulationInfluence of Fluctuations on Evolutionary DynamicsMauro Mobilia Evolutionary Game Theory: An Introduction, Lecture 2
Replicator DynamicsPopulation of Q different species: e 1 ,...,e Q , with frequencies x 1 ,...,x QState of the system described by x = (x 1 ,...,x Q ) ∈ S Q , whereS Q = {x;x i ≥ 0,∑ Q i=1 x i = 1}To set up the dynamics, we need a functional expression for thefitness f i (x)Between various possibilities, a very popular choice is:ẋ i = x i(fi (x) −¯f (x) ) ,where, one (out of many) possible choices, for the fitness is theexpected payoff: f i (x) = ∑ Q i=1 A ijx jand ¯f (x) is the average fitness: ¯f (x) = ∑ Q ix i f i (x)This choice corresponds to the so-called replicator dynamics onwhich most of evolutionary game theory is centeredMauro Mobilia Evolutionary Game Theory: An Introduction, Lecture 2
Page 1: An Introduction to Evolutionary Gam
Page 5 and 6: Some Properties of the Replicator D
Page 7 and 8: Replicator Dynamics for 2 × 2 Game
Page 9 and 10: Some Remarks on Replicator Dynamics
Page 11 and 12: Stochastic Dynamics & Moran Process
Page 13 and 14: Fixation in the Neutral & Constant
Page 15 and 16: Evolutionary Games in Finite Popula
Page 17 and 18: Influence of Fluctuations & Finite-
Page 19 and 20: Influence of Fluctuations & Finite-
Page 21 and 22: OutlookIn this set of lectures dedi

An Introduction to Evolutionary Game Theory: Lecture 2 - School of ...

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