TY - JOUR
T1 - Evolution, Population Growth, and History Dependence
AU - Sandholm, William H.
AU - Pauzner, Ady
PY - 1998/1
Y1 - 1998/1
N2 - We consider an evolutionary model with mutations which incorporates stochastic population growth. We provide a complete characterization of the effects of population growth on the evolution of play. In particular, we show that if the rate of population growth is at least logarithmic, the stochastic process describing play converges: only one equilibrium will be played from a certain point forward. If in addition the rate of mutation is taken to zero, the probability that the equilibrium selected is the first equilibrium played approaches one. Thus, population growth generates history dependence: the contingency of equilibrium selection on historical conditions.Journal of Economic LiteratureClassification Numbers: C72, C73, O33.
AB - We consider an evolutionary model with mutations which incorporates stochastic population growth. We provide a complete characterization of the effects of population growth on the evolution of play. In particular, we show that if the rate of population growth is at least logarithmic, the stochastic process describing play converges: only one equilibrium will be played from a certain point forward. If in addition the rate of mutation is taken to zero, the probability that the equilibrium selected is the first equilibrium played approaches one. Thus, population growth generates history dependence: the contingency of equilibrium selection on historical conditions.Journal of Economic LiteratureClassification Numbers: C72, C73, O33.
UR - http://www.scopus.com/inward/record.url?scp=0040599093&partnerID=8YFLogxK
U2 - 10.1006/game.1997.0575
DO - 10.1006/game.1997.0575
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AN - SCOPUS:0040599093
SN - 0899-8256
VL - 22
SP - 84
EP - 120
JO - Games and Economic Behavior
JF - Games and Economic Behavior
IS - 1
ER -