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Indirect Evolutionary Approach

Jörg Oechssler University of Heidelberg November 20, 2018

Jörg Oechssler University of Heidelberg () November 20, 2018 1 / 21

Literature

Güth, W. and Yaari, M. (1992). An evolutionary approach to explain reciprocal behavior in a simple strategic game, in (U. Witt, ed.), Explaining Process and Change – Approaches to Evolutionary Economics, 23–34, University of Michigan Press. Dekel, E., Ely, J. and Yilankaya, O. (2007). Evolution of Preferences, ReStud. Ely, J. and Yilankaya, O. (2001). Nash equilibrium and the evolution of preferences, JET. Huck, S. and Oechssler, J. (1999). The indirect evolutionary approach to explaining fair allocations, GEB. Huck, Kirchsteiger, Oechssler (2005), Learning to like what you have: Explaining the endowment e¤ect, Economic Journal.

Jörg Oechssler University of Heidelberg () November 20, 2018 2 / 21

Literature

Ok, E. and Vega-Redondo, F. (2001). On the evolution of individualistic preferences: an incomplete information scenario, JET. JET special issue 2001. Alger, I., and Weibull, J. (2013): Homo Moralis –Preference Evolution under Incomplete Information and Assortativity. Econometrica. Survey: Alger I. and Weibull, J. (2018), Evolutionary Models of Preference Formation, mimeo.

Jörg Oechssler University of Heidelberg () November 20, 2018 3 / 21

Direct vs. indirect evolution

(Direct) evolutionary approach: players are programmed to use certain strategies Payo¤ in game = …tness (e.g. number of descendants) Frequency of strategies in pop. changes according to …tness ESS ) Nash eq., dynamic e.g. replicator dynamic

Jörg Oechssler University of Heidelberg () November 20, 2018 4 / 21

Direct vs. indirect evolution

(Direct) evolutionary approach: players are programmed to use certain strategies Payo¤ in game = …tness (e.g. number of descendants) Frequency of strategies in pop. changes according to …tness ESS ) Nash eq., dynamic e.g. replicator dynamic Indirect evolutionary approach: players choose their strategies fully rationally given their preferences Distinction between …tness (based on material payo¤s) and utility, may like things that are not good for you Evolution of preferences, based on …tness or material payo¤s

Jörg Oechssler University of Heidelberg () November 20, 2018 4 / 21

Direct vs. indirect evolution

Why would evolution not allign preferences with …tness? Why do we blush when lying? Why do we get angry in the ultimatum game and reject unfair

• ¤ers?

Why do we have an endowment e¤ect?

Jörg Oechssler University of Heidelberg () November 20, 2018 5 / 21

Direct vs. indirect evolution

Why would evolution not allign preferences with …tness? Why do we blush when lying? Why do we get angry in the ultimatum game and reject unfair

• ¤ers?

Why do we have an endowment e¤ect?

Jörg Oechssler University of Heidelberg () November 20, 2018 6 / 21

A simple example: Cournot

C S-F S-L C 4,4 6,2 1,1 S-F 2,6 5,5 2,5 S-L 1,1 5,2

• 1,-1

Unique Nash eq. (C,C)

Jörg Oechssler University of Heidelberg () November 20, 2018 7 / 21

A simple example: Cournot

C S-F S-L C 4,4 6,2 1,1 S-F 2,6 5,5 2,5 S-L 1,1 5,2

• 1,-1

Unique Nash eq. (C,C) If a mutant could commit to Stackelberg leader strategy, would get 5

Jörg Oechssler University of Heidelberg () November 20, 2018 7 / 21

A simple example: Cournot

C S-F S-L C 4,4 6,2 1,1 S-F 2,6 5,5 2,5 S-L 1,1 5,2

• 1,-1

Unique Nash eq. (C,C) If a mutant could commit to Stackelberg leader strategy, would get 5 Suppose mutant‘s preferences deviate from material payo¤s s.t. U(S-L, y) = 7, 8y. S-L becomes dominant strategy

Jörg Oechssler University of Heidelberg () November 20, 2018 7 / 21

A simple example: Cournot

C S-F S-L C 4,4 6,2 1,1 S-F 2,6 5,5 2,5 S-L 1,1 5,2

• 1,-1

Unique Nash eq. (C,C) If a mutant could commit to Stackelberg leader strategy, would get 5 Suppose mutant‘s preferences deviate from material payo¤s s.t. U(S-L, y) = 7, 8y. S-L becomes dominant strategy Resident would give in: Outcome in material payo¤ is (5,2) better for mutant than Nash eq.

Jörg Oechssler University of Heidelberg () November 20, 2018 7 / 21

A simple example: Cournot

C S-F S-L C 4,4 6,2 1,1 S-F 2,6 5,5 2,5 S-L 1,1 5,2

• 1,-1

Unique Nash eq. (C,C) If a mutant could commit to Stackelberg leader strategy, would get 5 Suppose mutant‘s preferences deviate from material payo¤s s.t. U(S-L, y) = 7, 8y. S-L becomes dominant strategy Resident would give in: Outcome in material payo¤ is (5,2) better for mutant than Nash eq. Note: Observability of preferences!

Jörg Oechssler University of Heidelberg () November 20, 2018 7 / 21

A simple example: Cournot

C S-F S-L C 4,4 6,2 1,1 S-F 2,6 5,5 2,5 S-L 1,1 5,2

• 1,-1

Example only works if prefs are observable If not, residents must treat everyone equally, cannot make exception for rare mutants

Jörg Oechssler University of Heidelberg () November 20, 2018 8 / 21

A simple example: Cournot

C S-F S-L C 4,4 6,2 1,1 S-F 2,6 5,5 2,5 S-L 1,1 5,2

• 1,-1

Example only works if prefs are observable If not, residents must treat everyone equally, cannot make exception for rare mutants Mutants would get material payo¤ of 1

Jörg Oechssler University of Heidelberg () November 20, 2018 8 / 21

A simple example: Cournot

C S-F S-L C 4,4 6,2 1,1 S-F 2,6 5,5 2,5 S-L 1,1 5,2

• 1,-1

Example only works if prefs are observable If not, residents must treat everyone equally, cannot make exception for rare mutants Mutants would get material payo¤ of 1 In strategic situations: prefs that deviate from material prefs can be useful as commitment device. Frank (1988): „Passions with reason“: some of nature‘s signs (blushing, rage etc.) cannot easily be faked.

Jörg Oechssler University of Heidelberg () November 20, 2018 8 / 21

A general framework (Alger/Weibull)

Symmetric game (can be symmetrized): Γ = fn, X, πg

Jörg Oechssler University of Heidelberg () November 20, 2018 9 / 21

A general framework (Alger/Weibull)

Symmetric game (can be symmetrized): Γ = fn, X, πg X set of strategies (pure or mixed) π(xi, xi) material payo¤ function

π is continuous π is aggregative, i.e. invariant to permutatuions of xi. For simplicity assume 2-player game.

Jörg Oechssler University of Heidelberg () November 20, 2018 9 / 21

A general framework (Alger/Weibull)

Symmetric game (can be symmetrized): Γ = fn, X, πg X set of strategies (pure or mixed) π(xi, xi) material payo¤ function

π is continuous π is aggregative, i.e. invariant to permutatuions of xi. For simplicity assume 2-player game.

Type space: Θ. Types are continuous utility functions f : X 2 ! R (which can deviated from π) Evolution operates on types according to the material payo¤ they obtain. Types are inherited from one generation to the next. Types may or may not be private information

Jörg Oechssler University of Heidelberg () November 20, 2018 9 / 21

A general framework (Alger/Weibull)

Since strictly increasing transformations represents the same prefs, call [f ] the equivalence class of f . All g 2 [f ] have the same best replies.

Jörg Oechssler University of Heidelberg () November 20, 2018 10 / 21

A general framework (Alger/Weibull)

Since strictly increasing transformations represents the same prefs, call [f ] the equivalence class of f . All g 2 [f ] have the same best replies. In fact, focus on type homogeneous (Baysian) Nash equilibria: all indiv. of type g use the same strategy. But other types may also have overlapping best replies.

Jörg Oechssler University of Heidelberg () November 20, 2018 10 / 21

A general framework (Alger/Weibull)

Let Xf X denote the set of symmetric Nash equilibrium strategies ˆ x 2 arg max

x2X f (x, ˆ

x)

Jörg Oechssler University of Heidelberg () November 20, 2018 11 / 21

A general framework (Alger/Weibull)

Let Xf X denote the set of symmetric Nash equilibrium strategies ˆ x 2 arg max

x2X f (x, ˆ

x) Types that are “behaviorally distinct from f ”: Df :=

• g 2 F : arg max

x2X g(x, ˆ

x) \ arg max

x2X f (x, ˆ

x) = ?, 8ˆ x 2 Xf

• If everyone else plays some ˆ

x 2 Xf , a type g would never choose a strategy that can rationally be chosen by a type f .

Jörg Oechssler University of Heidelberg () November 20, 2018 11 / 21

Evolutionary stability of preferences

Focus on population states with a resident f (share 1 ε) and a mutant g (share ε) : (f , g, ε)

Jörg Oechssler University of Heidelberg () November 20, 2018 12 / 21

Evolutionary stability of preferences

Focus on population states with a resident f (share 1 ε) and a mutant g (share ε) : (f , g, ε) Let Π(f , g, ε) be the set of average material payo¤s

( ¯

πR, ¯ πM) in some type homogeneous (Bayesian) NE

Jörg Oechssler University of Heidelberg () November 20, 2018 12 / 21

Evolutionary stability of preferences

Focus on population states with a resident f (share 1 ε) and a mutant g (share ε) : (f , g, ε) Let Π(f , g, ε) be the set of average material payo¤s

( ¯

πR, ¯ πM) in some type homogeneous (Bayesian) NE

De…nition

Resident f is evolutionary stable against mutant g if 9¯ ε > 0, s.t. ¯ πR > ¯ πM,8( ¯ πR, ¯ πM) 2 Π(f , g, ε) and 8ε 2 (0, ¯ ε). f is evolutionary stable in Θ if it is evolutionary stable against all g 2 Θn[f ]. f is evolutionary unstable if there is a g and ¯ ε > 0, s.t.

8ε 2 (0, ¯

ε) there is some ( ¯ πR, ¯ πM) 2 Π(f , g, ε) with ¯ πR < ¯ πM.

Jörg Oechssler University of Heidelberg () November 20, 2018 12 / 21

Where Homo oeconomicus prevails

In a decision problem (game against nature) deviating from material payo¤s doesn‘t make sense (as nature does not react to you) π(xi, xi) = v(xi)

Jörg Oechssler University of Heidelberg () November 20, 2018 13 / 21

Where Homo oeconomicus prevails

In a decision problem (game against nature) deviating from material payo¤s doesn‘t make sense (as nature does not react to you) π(xi, xi) = v(xi)

Fact

In decision problems, Homo oeconomicus (i.e. [f ] = [π]) is evolutionary stable against all g 2 Dπ. Furthermore, all g 2 Dπ are evolutionary unstable.

Jörg Oechssler University of Heidelberg () November 20, 2018 13 / 21

Where Homo oeconomicus prevails

Suppose preferences are unobservable, private info

Jörg Oechssler University of Heidelberg () November 20, 2018 14 / 21

Where Homo oeconomicus prevails

Suppose preferences are unobservable, private info Matching is uniform and continuum population: Pr[f jf , ε] = Pr[f jg, ε]

Jörg Oechssler University of Heidelberg () November 20, 2018 14 / 21

Where Homo oeconomicus prevails

Suppose preferences are unobservable, private info Matching is uniform and continuum population: Pr[f jf , ε] = Pr[f jg, ε] For ε ! 0, must play NE of material game

Fact

Under uniform random matching in a continuum population, Homo

• economicus is evolutionary stable against all g 2 Dπ if preferences

are unobservable. Furthermore, all g 2 Dπ are evolutionary unstable. Lit.: Ok, Vega-Redondo (JET, 2001), Ely, Yilankaya (JET, 2001), Dekel et al. (ReStud, 2007), Alger, Weibull (Econometrica, 2013). But: su¢cient if prefs are observable sometimes (Güth, IJGT, 1995)

Jörg Oechssler University of Heidelberg () November 20, 2018 14 / 21

Where Homo oeconomicus is outperformed

Suppose preferences are observable Matching is uniform and continuum population

Jörg Oechssler University of Heidelberg () November 20, 2018 15 / 21

Where Homo oeconomicus is outperformed

Suppose preferences are observable Matching is uniform and continuum population Finite two-player games x 2 X is e¢cient if π(x, x) π(y, y), 8y 2 X.

Jörg Oechssler University of Heidelberg () November 20, 2018 15 / 21

Where Homo oeconomicus is outperformed

Suppose preferences are observable Matching is uniform and continuum population Finite two-player games x 2 X is e¢cient if π(x, x) π(y, y), 8y 2 X. Dekel et al. (ReStud, 2007) use slightly di¤erent def. of “stable con…gurations”

Fact

Under uniform random matching in a continuum population and with

• bservable preferences, a con…guration is stable only if the outcome

is e¢cient. If an outcome is e¢cient and a strict NE, then it is a stable con…guration.

Jörg Oechssler University of Heidelberg () November 20, 2018 15 / 21

Where Homo oeconomicus is outperformed

Similar results for continuum strategy spaces by Bester and Güth (JEBO, 1998), Possajennikov (JEBO, 2000): Homo

• economicus is unstable if material payo¤s are strategic

complements (altruism emerges) or substitutes (spite emerges)

Jörg Oechssler University of Heidelberg () November 20, 2018 16 / 21

Where Homo oeconomicus is outperformed

Similar results for continuum strategy spaces by Bester and Güth (JEBO, 1998), Possajennikov (JEBO, 2000): Homo

• economicus is unstable if material payo¤s are strategic

complements (altruism emerges) or substitutes (spite emerges) General result by Heifetz, Shannon, Spiegel (JET, 2007): Homo

• economicus will be outperformed in “almost all” games

See also: Alger, Weibull (J of Theor. Biology, 2012)

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Why do we have an endowment e¤ect?

Goods we own are more valuable: WTA > WTP (mug experiment, Kahneman, Knetsch, Thaler, JPE, 1990)

Jörg Oechssler University of Heidelberg () November 20, 2018 17 / 21

Why do we have an endowment e¤ect?

Goods we own are more valuable: WTA > WTP (mug experiment, Kahneman, Knetsch, Thaler, JPE, 1990) Suppose in past bargaining instead of markets

Jörg Oechssler University of Heidelberg () November 20, 2018 17 / 21

Why do we have an endowment e¤ect?

Goods we own are more valuable: WTA > WTP (mug experiment, Kahneman, Knetsch, Thaler, JPE, 1990) Suppose in past bargaining instead of markets If I can credibly signal that goods I own are more valuable to me, get better deal

Jörg Oechssler University of Heidelberg () November 20, 2018 17 / 21

Why do we have an endowment e¤ect?

Goods we own are more valuable: WTA > WTP (mug experiment, Kahneman, Knetsch, Thaler, JPE, 1990) Suppose in past bargaining instead of markets If I can credibly signal that goods I own are more valuable to me, get better deal Huck, Kirchsteiger, Oechssler (EJ, 2005): Nash bargaining solution (implicit: prefs observable)

Jörg Oechssler University of Heidelberg () November 20, 2018 17 / 21

Why do we have an endowment e¤ect?

Goods we own are more valuable: WTA > WTP (mug experiment, Kahneman, Knetsch, Thaler, JPE, 1990) Suppose in past bargaining instead of markets If I can credibly signal that goods I own are more valuable to me, get better deal Huck, Kirchsteiger, Oechssler (EJ, 2005): Nash bargaining solution (implicit: prefs observable)

Fact

If prefs are shaped by payo¤ positive dynamics (e.g. replicator), individuals with strictly positive endowment parameters will survive in the long run.

Jörg Oechssler University of Heidelberg () November 20, 2018 17 / 21

Indirect evolution of fairness in …nite populations

Can it be advantageous in terms of …tness to reject unfair o¤ers?

Jörg Oechssler University of Heidelberg () November 20, 2018 18 / 21

Indirect evolution of fairness in …nite populations

Can it be advantageous in terms of …tness to reject unfair o¤ers? Obviously yes if prefs observable. But mimicry? What if prefs not observable?

Jörg Oechssler University of Heidelberg () November 20, 2018 18 / 21

Indirect evolution of fairness in …nite populations

Can it be advantageous in terms of …tness to reject unfair o¤ers? Obviously yes if prefs observable. But mimicry? What if prefs not observable? Huck, Oechssler (GEB, 1999): analyze symmetrized game (sometimes proposer, sometimes responder).

Jörg Oechssler University of Heidelberg () November 20, 2018 18 / 21

Indirect evolution of fairness in …nite populations

Can it be advantageous in terms of …tness to reject unfair o¤ers? Obviously yes if prefs observable. But mimicry? What if prefs not observable? Huck, Oechssler (GEB, 1999): analyze symmetrized game (sometimes proposer, sometimes responder).

Fact

If the population is small enough, then all monotone evolutionary dynamics yield fair behavior in the long run. Intuition: A punishing indiv. meets one less punishing indiv. than the sel…sh individuals do. Also works if growing populations split up.

Jörg Oechssler University of Heidelberg () November 20, 2018 18 / 21

Homo moralis and assortative matching

Assortative matching: Pr[f jf , ε] 6= Pr[f jg, ε], e.g. mutants interact more often with each other

Jörg Oechssler University of Heidelberg () November 20, 2018 19 / 21

Homo moralis and assortative matching

Assortative matching: Pr[f jf , ε] 6= Pr[f jg, ε], e.g. mutants interact more often with each other Index of assortativity: σ := limε!0 (Pr[f jf , ε] Pr[f jg, ε]) = 1 limε!0 Pr[f jg, ε]

Jörg Oechssler University of Heidelberg () November 20, 2018 19 / 21

Homo moralis and assortative matching

Assortative matching: Pr[f jf , ε] 6= Pr[f jg, ε], e.g. mutants interact more often with each other Index of assortativity: σ := limε!0 (Pr[f jf , ε] Pr[f jg, ε]) = 1 limε!0 Pr[f jg, ε] Homo moralis has the utility function fκ(x, y) = (1 κ)π(x, y) + κπ(x, x) where κ is the degree of morality κ = 0: Homo oeconomicus κ = 1: Homo Kantientis (maximizes payo¤ under the assumption that everyone else chooses the same action, categorical imperative).

Jörg Oechssler University of Heidelberg () November 20, 2018 19 / 21

Homo moralis and assortative matching

Fact (Alger, Weibull, Econometrica, 2013)

Under assortative matching in a continuum population and unobservable preferences, Homo moralis with morality degree of κ = σ is evolutionary stable against all behaviorally distinct types and the latter are evolutionary unstable.

Jörg Oechssler University of Heidelberg () November 20, 2018 20 / 21

Homo moralis and assortative matching

Fact (Alger, Weibull, Econometrica, 2013)

Under assortative matching in a continuum population and unobservable preferences, Homo moralis with morality degree of κ = σ is evolutionary stable against all behaviorally distinct types and the latter are evolutionary unstable. Intuition: Let the resident be a Homo moralis playing ˆ x. Suppose a mutant enters. The best the mutant can do is to maximize the average material payo¤: ˆ y 2 arg max (σπ(y, ˆ y) + (1 σ)π(y, ˆ x))

Jörg Oechssler University of Heidelberg () November 20, 2018 20 / 21

Homo moralis and assortative matching

Fact (Alger, Weibull, Econometrica, 2013)

Under assortative matching in a continuum population and unobservable preferences, Homo moralis with morality degree of κ = σ is evolutionary stable against all behaviorally distinct types and the latter are evolutionary unstable. Intuition: Let the resident be a Homo moralis playing ˆ x. Suppose a mutant enters. The best the mutant can do is to maximize the average material payo¤: ˆ y 2 arg max (σπ(y, ˆ y) + (1 σ)π(y, ˆ x)) But this is exactly what Homo moralis is maximizing ˆ x 2 arg max (κπ(x, ˆ x) + (1 κ)π(x, ˆ y))

Jörg Oechssler University of Heidelberg () November 20, 2018 20 / 21

Example: PD

C D C 5,5 2,7 D 7,2 3,3 Let x =Prob(C) and σ = κ = 1/2

Jörg Oechssler University of Heidelberg () November 20, 2018 21 / 21

Example: PD

C D C 5,5 2,7 D 7,2 3,3 Let x =Prob(C) and σ = κ = 1/2 fκ(x, y) = 1

2π(x, y) + 1 2π(x, x) = x + 2y 1 2xy 1 2x2 + 3

Jörg Oechssler University of Heidelberg () November 20, 2018 21 / 21

Example: PD

C D C 5,5 2,7 D 7,2 3,3 Let x =Prob(C) and σ = κ = 1/2 fκ(x, y) = 1

2π(x, y) + 1 2π(x, x) = x + 2y 1 2xy 1 2x2 + 3

FOC: 1 1

2y x = 0. By symmetry (the resident meets almost

never a mutant), y = x ! ˆ x = 2/3.

Jörg Oechssler University of Heidelberg () November 20, 2018 21 / 21

Example: PD

C D C 5,5 2,7 D 7,2 3,3 Let x =Prob(C) and σ = κ = 1/2 fκ(x, y) = 1

2π(x, y) + 1 2π(x, x) = x + 2y 1 2xy 1 2x2 + 3

FOC: 1 1

2y x = 0. By symmetry (the resident meets almost

never a mutant), y = x ! ˆ x = 2/3. fκ(ˆ x, ˆ x) = 41

9 and π(ˆ

x, ˆ x) = 4

95 + 2 9(7 + 2) + 1 93 = 41 9

Jörg Oechssler University of Heidelberg () November 20, 2018 21 / 21

Example: PD

C D C 5,5 2,7 D 7,2 3,3 Let x =Prob(C) and σ = κ = 1/2 fκ(x, y) = 1

2π(x, y) + 1 2π(x, x) = x + 2y 1 2xy 1 2x2 + 3

FOC: 1 1

2y x = 0. By symmetry (the resident meets almost

never a mutant), y = x ! ˆ x = 2/3. fκ(ˆ x, ˆ x) = 41

9 and π(ˆ

x, ˆ x) = 4

95 + 2 9(7 + 2) + 1 93 = 41 9

π(D, ˆ x) = 1

2π(D, D) + 1 2

2

37 + 1 33

= 1

23 + 1 2 17 3 = 39 9

Jörg Oechssler University of Heidelberg () November 20, 2018 21 / 21