Evolutionary Game Theory
A.
Basic Concepts, notation & Definitions
2
ECON
461 Spring 2010,
H. Ofek
Evolutionary Games
Introduction
●
Evolutionary game theory is essentially the study of frequencydependent
selection (natural, or otherwise).
●
Expected payoffs are given in terms of expected fitness (expected number of
offspring that survive to reproductive age).
So, success in the game means
reproductive success.
●
The expected fitness of an individual depends on the frequency in which its
own (pheno) type is represented in the population, relative to other (pheno)
types.
●
The typical (but not exclusive) setting is a single population from which
members are randomly matched in pairs to play a 2player game (e.g., the
HawkDove game, among others).
●
Individuals are (genetically, or otherwise) programmed to play a fixed (pure
or mixed) strategy.
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3
ECON
461 Spring 2010,
H. Ofek
Evolutionary Games
Distinguishing Features
●
The following table summarizes some of the points that typically set evolutionary game
theory apart from conventional game theory.
●
It should be noted, however, that the mathematical structure of the games is essentially the
same and the solution concepts closely overlap.
Conventional Game Theory
Evolutionary Game Theory
Players are rational
Players are myopic
The apparatus of decision making is (Darwinian) natural
selection
Strategies are (genetically) encoded
Payoffs are in expected fitness
Sets of players are assigned to individual strategies
“Winners” and “losers” are populations (or subpopulation
groups)
Solution concept:
ESS – no rare mutant or invader can
survive
The apparatus of decision making is the human brain
Strategies are adapted by reason
Payoffs are in expected utility
Sets of strategies are assigned to individual players
“Winners” and “losers” are individual agents
Solution concept:
Nash equilibrium – no player can
unilaterally do better
4
ECON
461 Spring 2010,
H. Ofek
Evolutionary Games
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 Spring '08
 HAIMOFEK
 Game Theory, evolutionary game theory, Evolutionarily stable strategy, H. Ofek, Evolutionary games

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