Biomedical subjects

Drew Fudenberg

Publications and source records attributed to Drew Fudenberg.

4 recordsLinked to original sources

PubMed2006

Evolutionary game dynamics in finite populations with strong selection and weak mutation.

We study stochastic game dynamics in finite populations. To this end we extend the classical Moran process to incorporate frequency-dependent selection and mutation. For 2 x 2 games, we give a complete analysis of the long-run behavior when mutation rates are small. For 3 x 3 coordination games, we provide a simple rule to determine which strategy will be selected in large populations. The expected motion in our model resembles the standard replicator dynamics when the population is large, but is qualitatively different when the population is small. Our analysis shows that even in large finite populations the behavior of a replicator-like system can be different from that of the standard replicator dynamics. As an application, we consider selective language dynamics. We determine which language will be spoken in finite large populations. The results have an intuitive interpretation but would not be expected from an analysis of the replicator dynamics.

Biological Evolution↗

PubMed2005

Evolutionary cycles of cooperation and defection.

The main obstacle for the evolution of cooperation is that natural selection favors defection in most settings. In the repeated prisoner's dilemma, two individuals interact several times, and, in each round, they have a choice between cooperation and defection. We analyze the evolutionary dynamics of three simple strategies for the repeated prisoner's dilemma: always defect (ALLD), always cooperate (ALLC), and tit-for-tat (TFT). We study mutation-selection dynamics in finite populations. Despite ALLD being the only strict Nash equilibrium, we observe evolutionary oscillations among all three strategies. The population cycles from ALLD to TFT to ALLC and back to ALLD. Most surprisingly, the time average of these oscillations can be entirely concentrated on TFT. In contrast to the classical expectation, which is informed by deterministic evolutionary game theory of infinitely large populations, stochastic evolution of finite populations need not choose the strict Nash equilibrium and can therefore favor cooperation over defection.

Journal Article↗

PubMed2004

Emergence of cooperation and evolutionary stability in finite populations.

To explain the evolution of cooperation by natural selection has been a major goal of biologists since Darwin. Cooperators help others at a cost to themselves, while defectors receive the benefits of altruism without providing any help in return. The standard game dynamical formulation is the 'Prisoner's Dilemma', in which two players have a choice between cooperation and defection. In the repeated game, cooperators using direct reciprocity cannot be exploited by defectors, but it is unclear how such cooperators can arise in the first place. In general, defectors are stable against invasion by cooperators. This understanding is based on traditional concepts of evolutionary stability and dynamics in infinite populations. Here we study evolutionary game dynamics in finite populations. We show that a single cooperator using a strategy like 'tit-for-tat' can invade a population of defectors with a probability that corresponds to a net selective advantage. We specify the conditions required for natural selection to favour the emergence of cooperation and define evolutionary stability in finite populations.

Biological Evolution↗

PubMed2004

Evolutionary game dynamics in finite populations.

We introduce a model of stochastic evolutionary game dynamics in finite populations which is similar to the familiar replicator dynamics for infinite populations. Our focus is on the conditions for selection favoring the invasion and/or fixation of new phenotypes. For infinite populations, there are three generic selection scenarios describing evolutionary game dynamics among two strategies. For finite populations, there are eight selection scenarios. For a fixed payoff matrix a number of these scenarios can occur for different population sizes. We discuss several examples with unexpected behavior.

Biological Evolution↗