Evolutionary game theory analyzes animal behavior and evolution using game theory. It focuses on how strategy frequencies change over generations based on strategy payoffs. Key concepts include evolutionary stable strategies, where a strategy cannot be invaded by alternatives; sexual selection through mate choice; and cooperation evolving through kin selection. Game theory helps explain behaviors like aggression signaling, mate selection criteria, and how altruism can evolve.

1. An Introduction to...
Evolutionary Game Theory
[without complex
mathematics]
Dr. Karobi Moitra
BIOL 451 Evolution

2. What is Game Theory?
“Game theory is a study of how to
mathematically determine the best
strategy for given conditions in order to
optimize the outcome”
Find the best strategy to win!

3. Rationality
Assumptions:
• humans are rational beings
• humans always seek the best alternative in
a set of possible choices
Why assume rationality?
• narrow down the range of possibilities
• Predictability
When would you not choose the best
alternative?

4. Game Theory Involves
• Finding acceptable, if not
optimal, strategies in conflict situations.
• Game theory is highly mathematical
eg: Strategy for playing chess
• Game theory assumes all human
interactions can be understood and
navigated by presumptions.

5. Why is game theory important?
• All intelligent beings make decisions all the
time.
• Helps us to analyze situations more rationally
and formulate an acceptable alternative with
respect to circumstance.

6. The Party Planner
• Shelby is planning a party, and is worried
about whether it will rain or not
• The chances of rain are 33.3% on the day
of the party
• The party will be more fun outside
• How does Shelby come to a decision?

7. The Party Planner
• Outside – 1 (1/3 rd) ~33.3%
• Inside- 2 (2/3rds) ~66.6%
Where do you think Shelby will hold the
party if she makes the decision based on the
game theory?

10. The Party Planner
• She should hold it outside since there is
a 66% chance that it will not rain
However, if Shelby is a cautious person
she may hold it indoors or change the date
to account for the predicted weather

11. Basic Strategies
1. Plan ahead and look back
2. Use a dominating strategy if possible
3. Look for any equilibrium
4. Mix up the strategies

12. Game Theory?
http://www.youtube.com/watch?v=4S9a5V9ODuY
Hunger Games Trailer

16. Limitations & Problems
• Assumes players always maximize their
outcomes
• Some outcomes are difficult to provide a
utility for
• Not all of the payoffs can be quantified
• Not applicable to all problems

17. Brief History of Game Theory
• 1913 - E. Zermelo provided the first theorem of game theory
asserts that chess is strictly determined
• 1928 - John von Neumann proved the minimax theorem
• 1944 - John von Neumann / Oskar Morgenstern’s wrote
"Theory of Games and Economic Behavior”
• 1950-1953, John Nash describes Nash equilibrium
• 1972 - John Maynard Smith wrote
“Game Theory and The Evolution of Fighting”
http://william-king.www.drexel.edu/top/class/histf.html

18. John Nash
Not John Nash

19. Definition: Nash Equilibrium
“If there is a set of strategies with the property
that no player can benefit by changing her
strategy while the other players keep their
strategies unchanged, then that set of
strategies and the corresponding payoffs
constitute the Nash Equilibrium. “
Source: http://www.lebow.drexel.edu/economics/mccain/game/game.html

20. Nash Equilibrium
• Informally, a set of strategies is a Nash
equilibrium if no player can do better by
unilaterally changing his or her strategy
• It is the best strategy(ies)

21. Evolutionary Game Theory
“Evolutionary game theory differs from classical
game theory by focusing more on the dynamics
of strategy change as influenced not solely by
the quality of the various competing
strategies, but by the effect of the frequency
with which those various competing strategies
are found in the population”

22. Rock- Paper- Scissors
“An evolutionary game that turns out to be a
children’s game is rock-paper-scissors.
Anyone who has ever played this simple
game knows that it is not sensible to have any
favored play – your opponent will soon notice
this and switch to the winning counter-play. “

23. Rock-Paper-Scissors
“The best strategy (a Nash equilibrium) is to
play a mixed random game with any of the
three plays taken a third of the time. This, in
EGT terms, is a mixed strategy”

24. Game theory: when social conditions
determine behavioral strategies

25. Evolutionary Game Theory
• Natural selection replaces rational behavior
• Survival of the fittest

26. • http://www.youtube.com/watch?v=48EWLj3g
IJ8

27. Game Theory in Evolution
1. Evolutionary Stable Strategy (ESS)
2. Sexual Selection
3. Social Interactions and the Evolution of
Cooperation (Kin selection and altruism)

28. 1. Evolutionary Stable Strategy
“It is a Nash equilibrium that is
evolutionarily" stable: once it is fixed in a
population, natural selection alone is
sufficient to prevent alternative (mutant)
strategies from invading successfully. The
theory is not intended to deal with the
possibility of gross external changes to the
environment that bring new selective forces
to bear”

29. ESS
• An evolutionary stable strategy is a behavior
that, when adopted by a population of
players, cannot be invaded by an alternative
strategy

30. Evolutionary Stable Strategy
Is the winning strategy…

31. Evolutionary Stable Strategy
• Introduced by Maynard Smith and Price
(1973)
• Strategy becomes stable throughout the
population
• Mutations becoming ineffective

32. Hawk / Dove Game

33. Hawke – Dove Game
• The name "Hawk-Dove" refers to a situation in
which there is a competition for a shared
resource and the contestants can choose
either conciliation or conflict; this terminology
is most commonly used in biology and
evolutionary game theory.

34. • HAWK: very aggressive, always fights for some
resource.
• DOVE: never fights for a resource -- it displays
in any conflict and if it is attacked it
immediately withdraws before it gets injured.

35. • Thus, in any conflict situation, dove will always
lose the resource to a hawk, but it never gets
hurt (never sustains a decrease in fitness)
when confronting a hawk, and therefore the
interactions are neutral with respect to the
dove's fitness

36. • Imagine a Hawk only population
• Now imagine a Dove only population

37. •
•
•
•
Hawk only population- fighting and unrest
Dove only population- too peaceful
None is the ideal situation
None are ESS or in Nash Equilibrium

39. ESS
Many animals react aggressively or not depending on their opponents size or
correlated features
Male toads that clasps females before the eggs are laid and fertilized are often
aggressively displaced by larger males but not by smaller ones. A male is unlikely
to try to displace a mounted male that is larger than himself

40. Evolutionary Stable Strategy
Honest signals of the of the individual’s fighting ability or resource-holding
potential
Deceptive signals indicating greater fighting ability than the individual actually
has
Deceptive signals should be unstable in evolutionary time because selection
would favor genotypes that ignored the signals, which having lost their utility
would be lost in subsequent evolution
Dishonest signals
however are not
uncommon
Male fiddle crab
Uca annulipes

41. 2. Sexual Selection
Sexual Selection by mate choice:
The best mate should produce the best
offspring

42. Sexual Selection
Sexual Selection by mate choice
Sensory Bias
Certain traits may be intrinsically stimulating and evoke a greater response
simply because of the organization of the receptor’s sensory system
In some species of the fish
genus Xiphophorus part of the
male tail is elongated into a
“sword”
Females preferred males with
swords not only in
Xiphophorus but also in the
swordless genus Priapella

43. Sexual Selection
Sexual Selection by mate choice
Direct Benefit to Choosy Females
Male provides a direct benefit to the female or her offspring: nutrition, superior
territory, parental care
There is selection pressure on females to recognize males that are superior
providers
The preference selects for males with the distinctive correlated character

44. Sexual Selection
Sexual Selection by mate choice
Indirect Benefits of Mate Choice
Male provides no direct benefit to either the female or her offspring but
contributes only his genes
Alleles affecting female mate choice increase or decrease in frequency
depending on the fitness of the females’ offspring. Thus females may benefit
indirectly from their choice of mates

45. Sexual Selection
Sexual Selection by mate choice
GOOD GENES MODEL (HANDICAP HYPOTHESIS)
Because females risk substantial losses of fitness if their offspring do not survive
or reproduce, one could argue that females should evolve to choose males with
high genetic quality, so that their offspring will inherit “good genes” and so have
a superior prospect of survival and reproduction
Stickelback
Fish
Any male trait that is
correlated with genetic quality
(an indicator of good genes)
could be used by females as a
guide to advantageous
matings, so selection would
favor a genetic propensity in
females to choose mates on
this basis

46. 3. Social Interactions and the Evolution
of Cooperation
“Explaining how altruism –which by definition
reduces personal fitness– can arise by natural
selection is a major problem, and the central
theoretical problem of sociobiology”

47. 3. Social Interactions and the Evolution of Cooperation
Darwin’s theory of natural selection is based on individual advantage. Cooperative
interactions seem antithetical to evolution by natural selection and require
explanation
Until 1960’s it was common for biologists to assume that cooperation had evolved
because it benefited the population or species (group selection). The modern study
of cooperation focus on individual selection.

48. Social Interactions and the Evolution of Cooperation
Prisoner's Dilemma
C
S
Confess:
C
3
1
Silent: S
4
2

49. Social Interactions and the Evolution of Cooperation
Prisoner's Dilemma
The Prisoner's Dilemma game takes its name from the following scenario:
You and a criminal associate have been busted. Fortunately for you, most of the evidence was
shredded, so you are facing only a year in prison. But the prosecutor wants to nail someone, so he
offers you a deal: if you squeal on your associate –which will result in his getting a five year stretch–
the prosecutor will see that you are set free. Which sounds good, until you learn your associate is being
offered the same deal – which would get you five years

50. Social Interactions and the Evolution of Cooperation
To cooperate, or not cooperate? This simple
question, expressed in an extremely simple game, is a
crucial issue across a broad range of life
• Why shouldn't a barracuda eat the little fish that
has just cleaned it of parasites
• Fig wasps collectively limit the eggs they lay in fig
trees. But why shouldn't any one fig wasp cheat
and leave a few more eggs than her rivals?
• At the level of human society, why shouldn't each
of the villagers that share a common but finite
resource try to exploit it more than the others?
Yet barracudas, fig wasps, and villagers all cooperate. It
has been a constant problem in evolutionary studies to
explain how such cooperation should evolve, let alone
persist, in a world of self-maximizing egoists

51. Social Interactions and the Evolution of Cooperation
DIRECT BENEFITS: NON-ENFORCED
Cooperative behavior often evolves simply because it is advantageous to the
individual
Ex Joining flock or herd
Ex Unrelated helpers and delayed benefit
Pied kingfisher
Ceryle rudis

52. Social Interactions and the Evolution of Cooperation
INDIRECT BENEFITS: KIN SELECTION: KIN DISCRIMINATION AND CANNIBALISM
Many species of animals are cannibalistic preying on smaller individuals of the same
species. Many such species discriminate kin from non-kin and are less likely to eat
related individuals
Tadpoles develop into:
• Detritus and plant omnivores
Associate more with their siblings
• Cannibalistic carnivores
Associate more with nonrelatives
Carnivores eat siblings much less
frequently than unrelated
individuals
Spadefoot Toad
Scaphiopus bombifrons

53. Kin selection
Selection based on inclusive fitness
Hamilton’s Rule
An altruistic trait can increase in frequency if the
benefit (B) received by the donor’s relatives weighted
by their relatedness (r) to the donor, exceeds the cost
(C) of this trait to the donor’s fitness:
rB>C

54. In evolutionary biology, an organism is said to
behave altruistically when its behaviour
benefits other organisms, at a cost to itself.
The costs and benefits are measured in
terms of reproductive fitness, or expected
number of offspring. So by behaving
altruistically, an organism reduces the
number of offspring it is likely to produce
itself, but boosts the number that other
organisms are likely to produce

55. Social Interactions and the Evolution of Cooperation
SOCIAL INSECTS: ANT AND BEE COLONIES: VIDEO LINK- ALTRUISTIC WORKER BEES
HTTP://WWW.YOUTUBE.COM/WATCH?V=VSCMSWOF8PY
Eusocial animals Animals in which nearly or completely sterile individuals (workers)
rear the offspring of reproductive individuals , usually their parents
Known in Naked mole rat, termites, many hymenoptera
Naked Mole Rat
Heterocephalus glaber

56. Where is game theory currently used?
– Ecology
– Evolutionary
Biology
– Networks
– Economics
– Politics
– Conflict
– Business

57. Summary: Game Theory in Evolution
1. Evolutionary Stable Strategy (ESS)
2. Sexual Selection
3. Social Interactions and the Evolution of
Cooperation (Kin selection and altruism)

60. References
• Wikipedia
• http://williamking.www.drexel.edu/top/class/histf.html
•
http://www.lebow.drexel.edu/economics/mccain
/game/game.html
• SYMBOLIC SYSTEMS 202: The Rationality Debate
(3 units) Winter Quarter 2003-2004, Stanford
University Instructor: Todd Davies
(handout)
• Random .ppts from the internet- with no author
names to acknowledge