Week 4: Readings

Question 1

Five mechanisms for the evolution of

cooperation.

Answer 1

Kin selection operates when the
donor and the recipient of an altruistic act are
genetic relatives.
Direct reciprocity requires repeated encounters between the same two individuals.
Indirect reciprocity is based on reputation; a helpful individual is more likely to receive help.
Network reciprocity means that clusters of cooperators outcompete defectors.
Group selection is
the idea that competition is not only between
individuals but also between groups.

Question 2

Without any mechanism for the evolution

of cooperation, ___ dominate ___,

Answer 2

defectors dominate cooperators

Question 3

alt. mechanisms of cooperators

Answer 3

“green beard” models where cooperators recognize each other via arbitrary labels (56–58).
Another way to obtain cooperation is making the game voluntary rather than obligatory: If players can choose to cooperate, defect, or not play at all, then some level of
cooperation usually prevails in dynamic oscillations (59).

Question 4

conclusion

Answer 4

The two fundamental principles of evolution
are mutation and natural selection. But evolution
is constructive because of cooperation. New
levels of organization evolve when the competing units on the lower level begin to cooperate.
Cooperation allows specialization and thereby
promotes biological diversity. Cooperation is the
secret behind the open-endedness of the evolutionary process. Perhaps the most remarkable
aspect of evolution is its ability to generate cooperation in a competitive world. Thus, we
might add “natural cooperation” as a third fundamental principle of evolution beside mutation
and natural selection.

Question 5

natural selection without cooperation mechanisms favors…

Answer 5

In any mixed population, defectors
have a higher average fitness than cooperators
(Fig. 1). Therefore, selection acts to increase
the relative abundance of defectors. After some
time, cooperators vanish from the population.
Remarkably, however, a population of only
cooperators has the highest average fitness,
whereas a population of only defectors has
the lowest. Thus, natural selection constantly
reduces the average fitness of the population

Question 6

a cooperator is ….
a defector is…
reproduction can be…

Answer 6

A cooperator is someone who pays a cost,
c, for another individual to receive a benefit,
b. A defector has no cost and does not deal
out benefits. Cost and benefit are measured in
terms of fitness. Reproduction can be genetic
or cultural. I

Question 7

Fisher’s fundamental theorem, which

states that…

Answer 7

average fitness increases under
constant selection, does not apply here because selection is frequency-dependent: The
fitness of individuals depends on the frequency (= relative abundance) of cooperators in
the population. We see that natural selection in well-mixed populations needs help for establishing cooperation (because NS alone would favor defectors).

Question 8

Kin Selection

Answer 8

natural selection can favor cooperation if the
donor and the recipient of an altruistic act are
genetic relatives.

More precisely, Hamilton’s RULE
states that the coefficient of relatedness, r, must
exceed the cost-to-benefit ratio of the altruistic act:
r > c/b

Relatedness is defined as the probability of
sharing a gene. The probability that two brothers
share the same gene by descent is 1/2; the same
probability for cousins is 1/8. Hamilton’s theory
became widely known as “kin selection” or
“inclusive fitness”

*cooperation only among genetic relatives!

Question 9

Direct Reciprocity

Answer 9

cooperation between unrelated individuals or even between members of different
species.
repeated encounters between the same
two individuals.
In every round, each player has
a choice between cooperation and defection. If I
cooperate now, you may cooperate later. Hence,
it might pay off to cooperate. “winning strategy”
was the simplest of all, tit-for-tat. This strategy always starts with a cooperation, then it
does whatever the other player has done in the
previous round: a cooperation for a cooperation, a defection for a defection. this helps with quickly building cooperation in a society with mainly defectors but is replaced with win-stay, lose-shift.

Tit-for-tat cannot correct mistakes, because an accidental defection leads to a long sequence of retaliation.

generous-tit-for-tat (17), a strategy that cooperates whenever you cooperate,
but sometimes cooperates although you have
defected [with probability 1 − (c/b)]. Natural
selection can promote forgiveness.

win-stay, lose-shift, which is the even simpler
idea of repeating your previous move whenever you are doing well, but changing otherwise.

RULE:
Direct reciprocity can lead to the
evolution of cooperation only if the probability,
w, of another encounter between the same two
individuals exceeds the cost-to-benefit ratio of
the altruistic act:
w > c/b

*Direct reciprocity relies on
repeated encounters between the same two
individuals, and both individuals must be able
to provide help, which is less costly for the
donor than it is beneficial for the recipient.

Question 10

Indirect Reciprocity

Answer 10

used to explain interactions among humans are
asymmetric and fleeting. One person is in a
position to help another, but there is no possibility for a direct reciprocation. We help strangers
who are in need. We donate to charities that do
not donate to us.

indirect reciprocity is reputation

Helping someone establishes a good reputation, which will be rewarded by others. When
deciding how to act, we take into account the
possible consequences for our reputation.

where the same two individuals
need not meet again. One individual acts as
donor, the other as recipient. The donor can
decide whether or not to cooperate. The interaction is observed by a subset of the population who might inform others. Reputation
allows evolution of cooperation by indirect
reciprocity (19). Natural selection favors strategies that base the decision to help on the
reputation of the recipient

Indirect reciprocity has substantial cognitive
demands. Not only must we remember our own
interactions, we must also monitor the everchanging social network of the group. Language
is needed to gain the information and spread the
gossip associated with indirect reciprocity. Presumably, selection for indirect reciprocity and
human language has played a decisive role in
the evolution of human intelligence (28) reciprocity also leads to the evolution of morality
(30) and social norms (21, 22).

RULE:
Indirect reciprocity can
only promote cooperation if the probability, q,
of knowing someone’s reputation exceeds the
cost-to-benefit ratio of the altruistic act:
q > c/b

Question 11

Network Reciprocity

Answer 11

real populations are not
well mixed

Spatial structures or social networks imply that some individuals interact
more often than others. One approach of capturing this effect is evolutionary graph theory

A cooperator pays a cost, c, for
each neighbor to receive a benefit, b. Defectors have no costs, and their neighbors receive
no benefits. In this setting, cooperators can
prevail by forming network clusters, where
they help each other. The resulting “network
reciprocity” is a generalization of “spatial reciprocity” (40).

RULE:
he benefit-to-cost ratio must
exceed the average number of neighbors, k, per
individual:
b/c > k

Question 12

Group Selection

Answer 12

Selection acts not only on individuals but also
on groups. A group of cooperators might be
more successful than a group of defectors.

A simple model of group selection works as
follows (51). A population is subdivided into
groups. Cooperators help others in their own
group. Defectors do not help. Individuals reproduce proportional to their payoff. Offspring
are added to the same group. If a group reaches
a certain size, it can split into two. In this case,
another group becomes extinct in order to constrain the total population size. Note that only
individuals reproduce, but selection emerges
on two levels. There is competition between
groups because some groups grow faster and
split more often. In particular, pure cooperator
groups grow faster than pure defector groups,
whereas in any mixed group, defectors reproduce faster than cooperators. Therefore, selection on the lower level (within groups) favors
defectors, whereas selection on the higher level
(between groups) favors cooperators. This model
is based on “group fecundity selection,” which
means that groups of cooperators have a higher
rate of splitting in two. We can also imagine a
model based on “group viability selection,”where groups of cooperators are less likely to go
extinct.
In the mathematically convenient limit of
weak selection and rare group splitting, we obtain a simple result (51): If n is the maximum
group size and m is the number of groups, then
group selection allows evolution of cooperation,
provided that
b/c >1+(n/m)

Question 13

Evolutionary Success

Answer 13

Without any mechanism for the
evolution of cooperation, defectors dominate. A
mechanism for the evolution of cooperation can
allow cooperators to be the evolutionarily stable
strategy (ESS), risk-dominant (RD), or advantageous (AD) in comparison with defectors.

Cooperators are ESS if they can resist invasion by
defectors

Cooperators are RD if the basin of
attraction of defectors is less than 1/2.

Cooperators are AD if the basin of attraction of
defectors is less than 1/3. In this case, the fixation probability of a single cooperator in a finite
population of defectors is greater than the inverse of the population size (for weak selection).

Some mechanisms allow cooperators to dominate defectors.

Question 14

levels of miscommunication:

Answer 14

i. At 0% of miscmunication copycat wins.
ii. At 50% of miscomunication no one wins.
iii. Between 1-9% of miscomunication copykitten wins.
iv. Between 10-49% of miscomunication cheaters win.
o A little bit of miscomunication (1-9%) is fine because people forgive but too much miscomunication and it spreads distrust (10-49%).

Question 15

three factors required for cooperation?

Answer 15

1. REPEAT INTERACTIONS
   Trust keeps a relationship going, but you need the knowledge of possible future repeat interactions before trust can evolve.
2. POSSIBLE WIN-WINS
   You must be playing a non-zero-sum game, a game where it’s at least possible that both players can be better off – a win-win.
3. LOW MISCOMMUNICATION
   If the level of miscommunication is too high, trust breaks down. But when there’s a little bit of miscommunication, it pays to be more forgiving.

Question 16

simpleton will win in what type of population and what strategy does this reflect?

Answer 16

Simpleton will win because they can exploit always cooperators which copycats will not do (is it the win-stay; lose-shift strategy in a cooperative society without defectors at 5% miscommunication).

Question 17

In a population with high defectors, copy kittens, copy cats, simpleton and randoms who will win?

Answer 17

copy kitten.

Question 18

the problem with copycats? how do we fix this?

Answer 18

Copycats cannot forgive mistakes and leads to a cycle of retaliation (cooperate-defect, defect-cooperate, defect-cooperate etc).

How to fix mistakes?
copy-kitten: who only defects if you cheat them x2 in a row.

Question 19

Changing the Payoff & explanation with zero sum thinking

Answer 19

o When the benifit for both cooperate (win-win) is
lower than always cheat dominates.
o Two explanation for this effect from Game theory:
 Zero-sum game:
• This is the sadly common belief that a gain for “us”
must come at a loss to “them”, and vice versa.
 Non-zero-sum game:
• This is when people make the hard effort to create a
win-win solution! (or at least, avoid a lose-lose)
Without the non-zero-sum game, trust cannot
evolve.

Question 20

The number of rounds

Answer 20

when there is one round, the defector wins. when there are multiple interactions people are more likely to cooperate (as long as the payoff ratio is high for a win-win)

In a group of always cooperate and one defector and one copy cat. We see that 1-5 rounds cheaters always win. We see that 6+ rounds copy cats win.

Question 21

mixed populations

Answer 21

o With a mixed group (cheaters, copy cats and always cooperate) copy cats outcompete cheaters (always defectors) because they collaborate with one another and give defectors a taste of their own medicine (= group selection; where all cooperative groups are stronger then all defector groups) they also outcompete always cooperaters because they get exploited by cheaters.
o In a mixed group (cheaters, copy cats, always cooperate, grudges and detectives) copy cats win but a few grudgers may stick around.

Question 22

factors that influence how much money you give in director game:

Answer 22

 Familiarity: the more familiar you are with someone
the more you like them and the more willing you are
to give them money.
 Anonymity: if you are not familar with them than you
are more likley to keep the money.
 Amount/Value Earned: if you have more money you
are more willing to share some of it with others, the
smaller the award it the more liley you’d want to
keep it all for yourself. Similarly, if the reward is
something you want your least likley to share but if
it’s something you do not care for you are more
willing to share.
 Personal Values: universalism vs. Power.
Universalism values of egalitarianism will be more
willing to share.