This document summarizes a presentation on evolutionary game theory and its implications. It discusses how evolutionary game theory provides an alternative paradigm to the standard economic approach of rational choice and equilibrium analysis. It outlines concepts such as evolutionarily stable strategies and how preferences and behaviors evolve over time through strategic interactions. A key result is that "homo moralis" preferences that balance self-interest and adherence to moral rules like Kant's categorical imperative are evolutionarily stable, while other preference types are unstable. This suggests humans naturally develop a balance between self-interest and morality.

1. EVOLUTIONARY GAMES
J¨orgen W. Weibull
New approaches to economic challenges
OECD Headquarters, Paris
April 25, 2014

2. Themes
1. The economics paradigm and evolutionary game theory
2. Evolutionarily stable strategies
3. Evolutionarily stable family ties: Max Weber meets Charles Darwin
4. Evolutionarily stable balance between self-interest and morality
5. Implications for economic analysis and policy

3. Background texts
[with lots of references to the literature]
• Weibull: Evolutionary Game Theory. MIT Press, 1995.
• Alger and Weibull: ”Kinship, incentives and evolution”,
American Economic Review, 2010.
• Alger and Weibull: ”Homo moralis - preference evolution under incom-
plete information and assortative matching”, Econometrica, 2013.

4. 1 The economics paradigm
• The main paradigm in economics is Bayesian and rationalistic. Foun-
dations:
— John von Neumann and Oskar Morgenstern (1944): Games and
Economic Behavior
— John Nash (1950): “Non-cooperative games”, Ph D thesis (Prince-
ton University)
— Leonard Savage (1954): The Foundations of Statistics

5. • Each economic agent’s behavior derived from maximization of some
goal function (utility, profit), under given constraints and information
• The ”as if” defence of this paradigm is evolutionary:
— Milton Friedman (1953): The Methodology of Positive Economics
— Firms that do not take profit-maximizing actions are selected against
in the market
— Is this claim right? Under perfect competition? Under imperfect
competition?

6. 2 The evolutionary paradigm
• Formulated by Charles Darwin and combined with game theory by John
Maynard Smith
— Darwin: non-strategic interactions, like perfect competition in eco-
nomics
— Maynard Smith: strategic interactions, like imperfect competition
in economics

7. 3 Three branches of game theory
• A mathematically formalized theory of strategic interaction
• Applications abound, in economics, political science, biology, and com-
puter science
• Non-cooperative, cooperative, and evolutionary game theory
• John Nash’s (1950) Ph D thesis in mathematics at Princeton (”A
Beautiful Mind”)
• Nash’s two interpretations: one rationalistic/individualistic,
one evolutionary/population-statistical

8. John Nash
(born 1928, PhD 1950)

9. Director: Ron Howard.
Main actors: Russell Crowe and Jennifer Connelly
Inspired by the 1998 book of the same name by Sylvia Nasar
The film won 4 Academy Rewards
A Beautiful Mind (2001)

10. Citation from Nash’s Ph D thesis∞
”We shall now take up the ”mass-action” interpretation of equi-
librium points. [...] It is unnecessary to assume that the partic-
ipants have full knowledge of the total structure of the game, or
the ability and inclination to go through any complex reasoning
processes. But the participants are supposed to accumulate em-
pirical information on the relative advantages of the various pure
strategies at their disposal.
To be more detailed, we assume that there is a population (in
the sense of statistics) of participants for each position of the
game. Let us also assume that the ”average playing” of the game
involves  participants elected at random from the  populations,
and that there is a stable average frequency with which each pure
strategy is employed by the ”average member” of the appropriate
population.

11. Since there is to be no collaboration between individuals playing
in different positions of the game, the probability that a particular
-tuple of pure strategies will be employed in a playing of the game
should be the product of the probabilities indicating the chance of
each of the  pure strategies to be employed in a random playing.
[...]
Thus the assumptions we made in this ”mass-action” interpreta-
tion lead to the conclusion that the mixed strategies representing
the average behavior in each of the populations form an equilib-
rium point.”

12. 4 Evolutionary game theory
Evolutionary process = mutation process + selection process
Unit of selection: usually strategies (”strategy evolution”), sometimes goal
functions (”preference evolution”, ”indirect evolution”)
Analytical tools for the researcher:
1. Evolutionary stability: focus on mutations
2. Replicator dynamic: focus on selection
3. Stochastic stability: both selection and mutations

13. 5 Evolutionarily stable strategies
[Maynard Smith and Price (Nature, 1973)]
Here the unit of selection, the heritable trait, is a behavior, a pure or mixed
strategy in a finite and symmetric two-player game
• ESS = evolutionarily stable strategy
— ”ESS” ≈ “a strategy that ‘cannot be overturned’ once it has be-
come the ‘convention’ in a population

16. Heuristically
1. A large population of individuals who are recurrently and uniformly
randomly matched in pairs to play a finite and symmetric two-player
game
2. Initially, all individuals always use the same pure or mixed strategy, ,
the incumbent (pure or mixed) strategy
3. Suddenly, a small population share  switch to another pure or mixed
strategy, , the mutant (pure or mixed) strategy

17. 4. If the residents/incumbents on average do better (in material payoffs,
fitness) than the mutants, then  is evolutionarily stable against 
5.  is evolutionarily stable if it is evolutionarily stable against all  6= 

18. Formally
A (pure or mixed) strategy  is an ESS if
(i)  is a best reply to itself, and
(ii)  is a better reply to all other best replies to  (than they are to
themselves)
⇒ ( ) must constitute a Nash equilibrium, and, in addition, ”fight back”
other best replies

19. 5.1 Examples
5.1.1 Prisoner’s dilemma
- To cooperate or defect?
- To fish aggressively in the common pool, or fish modestly?
 
 3 3 0 4
 4 0 2 2
• One ESS: play D. Cooperation is ruled out

20. 5.1.2 Coordination game
- To meet at the good restaurant or at the bad restaurant?
- To stick to the more efficient industrial standard or to the less efficient?
 
 2 2 0 0
 0 0 1 1
• Two ESSs: play A, or, alternatively, play B. The inefficient industrial
standard is not ruled out (but the mixed Nash-equilibrium strategy is
ruled out)

21. 5.1.3 Hawk-dove game
- Start-up business with two partners
- Pairs of researchers or workers assigned a common task
To work or shirk?
 
 3 3 0 4
 4 0 −1 −1
What will happen?

22. A unique strategy that is a best reply to itself: randomize 50/50 between
”work” and ”shirk” ∗ = (12 12)
This is an ESS if it is also a better reply to all other (pure or mixed)
strategies than they are to themselves
Can be verified that this is the case, by way of calculus
• One ESS: randomize 50/50 between work and shirk

23. 6 Extensions and generalizations
Based on joint work with Ingela Alger (Toulouse School of Economics and
Institute for Advanced Study in Toulouse),
Extend and generalize the notion of evolutionary stability!
(a) from a property of strategies (behaviors) to a property of preferences
and moral values (goal functions), and
(b) from uniform random matching to assortative random matching (here
mutants may be more likely to be matched with mutants)

24. • Evolutionary stability of family ties in symmetric pairwise interactions
between siblings (who know each other)
• Evolutionary stability of preferences and/or moral values in symmetric
pairwise interactions between strangers (who do not know each other)
• Evolutionary stability of preferences and/or moral values in symmetric
-player interactions between strangers

25. 7 Kinship, incentives and evolution (AER, 2010)
– or ”Max Weber meets Charles Darwin”
How much should one expect siblings to care for each other?
How does their caring influence their economic incentives?
• Particularly important when formal insurance institutions are absent or
weak
• Preferences inherited from biological or ”cultural” parents
• Represent family ties between siblings as a degree of altruism/spite

26. • Assume a sibling  attaches unit weight to his/her own material well-
being and weight  to the material well-being of sibling 
• Assume −1    +1
• Evolutionary biology (Hamilton’s rule), suggests siblings behave as if
 = 12 (their degree of relatedness)
• However, biologists then treat resources as exogenous (exchange econ-
omy), while in many situations resources are endogenous (production
economy)

27. Our model:
• sequential interactions between sibling pairs: individual production,
random outputs, voluntary transfers
• material outcomes drive evolutionary selection
• complete information: siblings know each other’s degree of altruism
*Note that there is assortative matching: if a sibling is a rare mutant, and altruism is
inherited from mother or father (with equal probability), then also the other sibling is a
mutant with proba. 1/2

28. Q: In a given environment: Is there an evolutionarily stable degree  of
altruism between siblings? If so, how large and on what does it depend?
A: There is anvolutionarily stable degree ∗ of sibling altruism, and ∗ 
12. Moreover, ∗ depends on the ”environment”: lower in harsher (Swe-
den) than in milder (Italy)

29. 8 Homo moralis
• Now consider evolutionary stability of preferences and/or moral values
when these are private information
• Unlike in the sibling study: make no assumption about the form of
preferences or moral values
• Assume that individuals adjust their behavior according to their per-
sonal preferences or moral values, so that play reaches a Nash equilib-
rium under incomplete information
• Allow for arbitrary assortative matching (with uniform matching and
siblings as special cases)

30. Q: What social preferences and/or moral values should one expect humans
to have from first principles?
A: The mathematics leads to a new class of social preferences cum moral
values, those of homo moralis
• Homo moralis is torn between
— self-interest and
— morality in line with Kant’s categorical imperative
• Homo oeconomicus the special case when all focus is on self interest,
with no regard to morality
• We will show that, in a theoretical sense, homo oeconomicus is in fact
rare

31. Kant’s categorical imperative
“Act only according to that maxim whereby you can,
at the same time, will that it should become a universal law”
[Grundlegung z¨ur Metaphysik der Sitten, 1785]

32. Immanuel Kant
(1724 – 1804)

33. 8.1 Pairwise interactions
• Individuals randomly matched into pairs
• Each pair plays a symmetric game in material payoffs
• Material payoff  ( ) from using strategy  against  (where  is
continuous)
• Material payoff outcomes drive evolution

34. • Each individual has a type , which defines a continuous goal function
 ( )
— The goal function may, but need not, depend on (own and others’)
material payoffs
• The type set Θ is rich: it contains all continuous goal functions, in-
cluding that of homo oeconomicus,  = 
• Each individual’s type is his/her private information
• Each matched pair plays a game of incomplete information

35. • The probabilistic type-profile in a given individual’s matches may de-
pend on whether she is a mutant or not
• Let  ∈ [0 1] be the probability, for a given mutant, that the other
party is another mutant, when mutants are vanishingly rare
•  is called the index of assortativity (Bergstrom, American Economic
Review 2003)
— Uniform random matching:  = 0
— Siblings:  = 05
— ”Cultural parents,” and homophyly: 0    1

36. Definitions from Alger and Weibull (2013):
• A type  is evolutionarily stable if rare mutants fare strictly worse (in
material payoffs) than residents in all (Bayesian) Nash equilibria
• A type  is evolutionarily unstable if ∃ a mutant type  that fares
strictly better (in material payoffs) in all (Bayesian) Nash equilibria
• Given any type  ∈ Θ, a behavioral clone is a type 0 ∈ Θ that, as rare
mutant among -individuals, behaves exactly like 

37. 8.2 Main result
[Alger and Weibull, 2013]
Theorem 8.1 Suppose the equilibrium behavior of homo moralis, in the
absence of mutants, is uniquely determined. Then
(a) Homo moralis with degree of morality  is evolutionarily stable against
all types that are not its behavioral clones.
(b) All types that are not its behavioral clones are evolutionarily unstable.
• So, what, exactly, is a ”homo moralis”? And what is the ”degree of
morality”?

38. Definition 8.1 A homo moralis is an individual with utility function
 ( ) = (1 − ) ·  ( ) +  ·  ( )
for some  ∈ [0 1], her degree of morality.
• Homo oeconomicus:  = 0
• Homo kantientis:  = 1
• Homo moralis is torn between selfishness and Kantian morality:
— maximization of own material payoff
— “doing the right thing, in terms of material payoffs, if upheld as a
universal law”

39. • Intuition for the stability result: HM with  =  preempts mutants;
does what the most threatening mutant would do
• Intuition for the instability of other types: for any other type there will
exist a mutant type who is ”committed” to a strategy/behavior that
fares better (in material terms) and can thus ”break in”

40. 8.3 Taking homo moralis for a short ride
Prisoner’s dilemma
Two homo moralis of equal degree of morality
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.5
1.0
kappa
Pr(C)

41. Dictator game
Two homo moralis of equal degree of morality
• Random resource allocation so that one is “rich” and one “poor”, with
equal probability for both
• The rich individual decides (dictatorially) how much to give (if at all)
to the poor individual
• A strategy  is the amount to give if rich
• Continuous, strictly increasing and strictly concave indirect utility of
money (=material payoff)

42. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0
1
2
3
4
5
6
kappa
x

43. 9 Interactions in groups of arbitrary size
• The same result seems to hold for symmetric interactions for any num-
ber  ≥ 2 of players
• The notions of symmetry, assortative matching and the definition of
homo moralis need to be worked out
• Work in progress, see our WP (2014)

44. 10 Implications for economic analysis and policy
1. Evolutionary game theory asks for more than equilibrium; also robust-
ness against ”rare mutations” is asked for, and this can drastically
reduce the set of outcomes.
(a) The efficient equilibrium in coordination games: (i) evolutionary
stability and pre-play communication (Arthur Robson), (ii) ”sto-
chastic stability” (Peyton Young)
(b) The Nash bargaining solution as a result of evolution (”stochastic
stability”, Peyton Young)
2. Evolutionary stability of family ties, with implications for economic
incentives, can be relevant for economic history and development eco-
nomics. (Ingela Alger is working on such a project with economists in
Mexico.)

45. 3. Our homo moralis can potentially make a difference in many areas of
economics and social science, and for policy analysis:
(a) Environmental economics: conventional analysis assumes that in-
dividuals may care about their marginal effects on the environment,
but not what would be ”the right thing to do” if others did likewise
(b) Bargaining, contracts, moral hazard: conventional analysis assumes
pure self-interest, not that parties might, to some extent, also care
about what is ”the right thing to do” [However: see Edgeworth
1881!]
(c) Participation and voting in elections: conventional analysis assumes
that voters only consider the probability of being pivotal and the
cost of voting, not what would be ”the right thing to do” etc.

46. 11 Conclusions
• Our analysis suggests that selfishness is evolutionarily stable only in
special circumstances, while homo moralis with degree of morality
equal to the index of assortativity is always evolutionarily stable
• Moral preferences may thrive, even under incomplete information and
even in interactions in large groups (even infinite)
• Our analysis permits a new interpretation of Maynard Smith’s and
Price’s ESS - as equilibrium play by homo moralis under incomplete
information
• Lots of new challenges: extensions, applications, tests in laboratory
experiments and on field data...

47. THE END