
CMUCS03155
Computer Science Department
School of Computer Science, Carnegie Mellon University
CMUCS03155
An Evolutionary Resolution to the Finitely
Repeated Prisoner's Dilemma Paradox
Daniel B. Neill
June 2003
CMUCS03155.ps
CMUCS03155.pdf
Keywords: Game theory, evolutionary games, Finitely Repeated
Prisoner's Dilemma
Argument by backward induction forces us to conclude that two "rational"
players will defect on every turn of the Finitely Repeated Prisoner's
Dilemma (FRPD) game, thus performing significantly worse than agents with
imperfect rationality. When this game is treated from an evolutionary
perspective, using the standard evolutionary model, we encounter a similar
paradox: a population which cooperates through turn k can be invaded by a
strategy which cooperates through turn k1, and this process continues
until the population is dominated by defectors. However, though the
strategy of continual defection is evolutionarily stable, it is inferior
to nearly all other FRPD strategies: a bistable equilibrium occurs, in
which a very small proportion of the other strategy can take over the
population. Thus we propose and defend an alternative evolutionary model,
a random invasion model in which "evolutionary dominance" is used instead
of Maynard Smith's invasion criteria. This model combines the Lamarckian
spread of ideas through a population with Darwinian natural selection of
the organisms adopting those ideas, and thus is a more reasonable model of
communicating populations. When the new evolutionary model is
applied to the Finitely Repeated Prisoner's Dilemma, we find that
defectors dominate
the population for very short FRPD games, but as game length increases, it
becomes more and more certain that successful strategies will cooperate
until near the end of the game. Defining rationality based on
evolutionary fitness (or fictitious evolutionary play) using this model,
we achieve a resolution to the Finitely Repeated Prisoner's Dilemma
paradox. Additionally, the model can be generalized and applied to many
other decision situations, and thus it serves as a possible standard for
rational decisionmaking under uncertainty.
21 pages
