Indirect Evolutionary Approach Jrg Oechssler University of - PowerPoint PPT Presentation

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 o¤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 o¤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, 8 y . 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, 8 y . 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, 8 y . 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 = f n , X , π g Jörg Oechssler University of Heidelberg () November 20, 2018 9 / 21

A general framework (Alger/Weibull) Symmetric game (can be symmetrized): Γ = f n , X , π g X set of strategies (pure or mixed) π ( x i , x � i ) material payo¤ function π is continuous π is aggregative, i.e. invariant to permutatuions of x � i . 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 = f n , X , π g X set of strategies (pure or mixed) π ( x i , x � i ) material payo¤ function π is continuous π is aggregative, i.e. invariant to permutatuions of x � i . 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 X f � X denote the set of symmetric Nash equilibrium strategies x 2 arg max ˆ x 2 X f ( x , ˆ x ) Jörg Oechssler University of Heidelberg () November 20, 2018 11 / 21

A general framework (Alger/Weibull) Let X f � X denote the set of symmetric Nash equilibrium strategies x 2 arg max ˆ x 2 X f ( x , ˆ x ) Types that are “behaviorally distinct from f ”: � � D f : = g 2 F : arg max x 2 X g ( x , ˆ x ) \ arg max x 2 X f ( x , ˆ x ) = ? , 8 ˆ x 2 X f If everyone else plays some ˆ x 2 X f , 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 ( ¯ π R , ¯ π M ) in some type homogeneous (Bayesian) NE Jörg Oechssler University of Heidelberg () November 20, 2018 12 / 21