Ethics, Evolution, and Games among Family and Neighborsecon.ucsb.edu/~tedb/Lectures/Brentalk.pdf · Ethics, Evolution, and Games among Family and Neighbors Ted Bergstrom April, 2009

Ethics, Evolution, and Gamesamong Family and Neighbors

Ted Bergstrom

April, 2009

Ted Bergstrom Ethics, Evolution, and Games among Family and Neighbors

Golden Rule Maxims

• Religions and philosophies offer several maxims known as “goldenrules”.

• These rules sound similar, but have different implications for behaviorin some games.

• We analyze these differences and show how they relate to cultural andbiological evolution.


Love-thy-neighbor rules:

• “Thou shalt love thy neighbor as thyself.”Old testament–Leviticus 19:18

• Taoist: “Regard your neighbor’s gain as your gain, and yourneighbor’s loss as your loss.”


Do-unto-other-rules

• “Do unto others as you would have them do unto you.”New testament–Luke 6:31

• Aristotle: “We should behave toward friends as we would wish friendsto behave toward us.”

• Jainist: “A man should wander about treating all creatures as hehimself would be treated.”


Do-unto-other-rules

• “Do unto others as you would have them do unto you.”New testament–Luke 6:31

• Aristotle: “We should behave toward friends as we would wish friendsto behave toward us.”

• Jainist: “A man should wander about treating all creatures as hehimself would be treated.”


Negative do-unto-others-rules

• Confucius: “Never impose on others what you would not choose foryourself.”

• Talmud: “That which thou likest not being done unto thyself, do notdo unto thy neighbor. That is the whole of the Torah. The remainderis commentary. ”

• Buddhist: “Hurt not others in ways that you would find hurtful.”

• Hindu: “This is the sum of duty: do not do to others what wouldcause pain if done to you.”


Negative do-unto-others-rules

• Confucius: “Never impose on others what you would not choose foryourself.”

• Talmud: “That which thou likest not being done unto thyself, do notdo unto thy neighbor. That is the whole of the Torah. The remainderis commentary. ”

• Buddhist: “Hurt not others in ways that you would find hurtful.”

• Hindu: “This is the sum of duty: do not do to others what wouldcause pain if done to you.”


Rules of reciprocity

• Kant: “Act only according to the maxim whereby you can at thesame time will that it should become a universal law.”

• “Do for one who may do for you, that you may cause him thus to.”The Eloquent Peasant: Egyptian tale from 2000 B.C. (R.B. Parkinsontranslation from papyri.)




• “Do for one who may do for you, that you may cause him thus to.”

The Eloquent Peasant: Egyptian tale from 2000 B.C. (R.B. Parkinsontranslation from papyri.)




• “Do for one who may do for you, that you may cause him thus to.”The Eloquent Peasant: Egyptian tale from 2000 B.C. (R.B. Parkinsontranslation from papyri.)


Golden Rule Games

• Ethics are better understood if framed in a game.

• Assume that people have well-defined private payoffs and that goldenrules advise people on how to weigh others’ private preferences whenplaying in games.


Two person symmetric games

• There is a private payoff function u(x , y) such that if you play x andyour opponent plays y you get private payoff of u(x , y).

• Since the game is symmetric, if you play x and your opponent playsy , your opponent gets u(y , x).


Golden rule utility functions

• Love-thy-neighbor utility function:

L(x , y) = u(x , y) + u(y , x).

• Do-unto-others utility function:

D(x , y) = u(y , x).

• Kantian utility function

K (x , y) = u(x , x).




L(x , y) = u(x , y) + u(y , x).


D(x , y) = u(y , x).


K (x , y) = u(x , x).




L(x , y) = u(x , y) + u(y , x).


D(x , y) = u(y , x).


K (x , y) = u(x , x).


Negative Do-unto-others golden rule

• Define action x0 that “does no harm.”

• Act according to utility function

N(x , y) = u(x , y) if u(y , x) ≥ u(y , x0)

= −∞ if u(y , x) < u(y , x0).


The Christmas Gift Game

• Two friends, both drink cheap scotch. An expensive bottle costs $80,but is only worth $60 to either of them.

• Each considers buying expensive scotch as a gift for the other. Thereare two strategies. G “Give” and D “Don’t give”.

• Private payoff functions are: u(D, D) = 0, u(D, G ) = 60,u(G , D) = −80, u(D, D) = −20.

• It is dominant strategy for Do-unto-others-types to give the scotchsince u(x , G ) > u(x , D).

• It is dominant strategy for Love-thy-neighbor types not to give.Summed utilities highest no gift.

• Same goes for Kantians: U(D, D) > u(G , G ); Same for NegativeDo-unto-others

• So only the Do-unto-others types fall into the Christmas gift trap,and they are worse off for it.






































Redistribution Game

• Two neighbors: A coin is tossed. If heads, Neighbor A gets $100 andB gets $20. If tails, payoffs are reversed.

• After the coin toss, either can give any of his winnings to other.

• Both have concave utility functions. Each chooses a strategy of whatto do in each outcome.


Outcomes of redistribution game

• Love thy neighbor players and Kantian players would choose to give$40 if they win $100 and 0 if they win $20.

• No harm player would not give anything.

• Do unto others player would give his entire winnings.

• Final income distribution is equality in the first two cases and $20,$100 in the last two cases.


Love trumps reciprocity

• Private payoffs are determined by a symmetric prisoners’ dilemmagame–two strategies, c and d.

• u(d , c) = T , u(c , c) = R, u(d , d) = P, and u(c, d) = S whereT > R > P > S .

• Assume that T + S > 2R.

• Do-unto-others utility You would like others to do c, so you do c .D(c , x) = u(c , c) = R > P = u(d , d) = D(d , x).Same for Kantian utility u(c , c) > u(d , d), so both choose c , bothget R.

• Love-thy-neighbor utility.L(c , d) = L(d , c) = T + S > L(c , c) > L(d , d) = 2P. The Nashequilibria are (c , d) and (d , c), with total payoff T + S > 2R.
















Reciprocity trumps love

• Private payoffs are determined by the same symmetric prisoners’dilemma game.


• Assume this time that T + S < 2P.

• Do-unto-others utility and Kantian utility: As before, the only Nashequilibrium is (c, c).

• Love-thy-neighbor utility.L(c , d) = L(d , c) = T + S < L(d , d) = 2P < L(c , c). There are twoNash equilibria. One at (d , d) and one at (c , c).


Reciprocity trumps love

• Private payoffs are determined by the same symmetric prisoners’dilemma game.


• Assume this time that T + S < 2P.

• Do-unto-others utility and Kantian utility: As before, the only Nashequilibrium is (c, c).

• Love-thy-neighbor utility.L(c , d) = L(d , c) = T + S < L(d , d) = 2P < L(c , c). There are twoNash equilibria. One at (d , d) and one at (c , c).


Cultural selection

• Golden rules typically applied to dealings with neighbors: Long termrelationships with close observation.

• Folk theorem is that in such an environment, with perfect informationthere are many equilibria.

• Religions we know about are those of successful societies. Successfulsocieties coordinate on strategies that are socially efficient.

• Kantian rule picks best symmetric solution. But even in symmetricgames, efficient outcome may not be symmetric.


When are equilibria the same?

• Do golden rules predict the same symmetric Nash equilibria?

• First order conditions for (x̄ , x̄) to be a Nash equilibrium are the samefor Love-thy-neighbor and Kantian rules but not for Do-unto-others.

• Second order conditions are different for Love-thy-neighbor andKantian rules. In general, they can give different solutions. They willgive same solutions if u12 = 0, and more generally if u is a concavefunction of both its arguments.

• Love thy neighbor doesn’t ask “what if we both do it?” Kantian ruledoes. This can matter if u12 6= 0.


Less demanding rules

• In games of incomplete information, Kantian or Love-thy-neighborsolutions are not likely to be equilibria.

• Few people really abide by them.

• How about weaker rules?

• Confucius, the Talmud, the Hindus, and the Buddhists’ Don’t-do ruleis more modest. Doesn’t demand that rich share equally with poor.


Biology and Kin Selection

• Hamilton’s rule: Love thy neighbor r times as well as thyself, where ris thy coefficient of relatedness to that neighbor.

• Definition of Inclusive fitness for symmetric game with relative

I (x , y) = u(x , y) + ru(y , x).

• Not proscriptive, but predictive.

• Answers “who is my neighbor?”

• Less demanding than golden rules. For siblings r = 1/2, for cousinsr = 1/8. For strangers, r = 0.


Semi-Kantian rules

• Semi-Kantian rule: “Act as would be in your self-interest, if withprobability r , your neighbor will copy any action that you take.”

• V (x , y) = ru(x , x) + (1− r)u(x , y).

• Biological and cultural evolutionary models imply selection forbehavior x that is a symmetric Nash equilibrium for a game withpayoff function V .

• In biology, r is the probability that if you are a mutant, so is yourneighbor. Same idea works for cultural evolution.


Asymmetric Games:Genetics symmetrizes

• Big brother little brother game.

• Genes carry instructions for what to do if you are first-born, what todo if second-born.

• Gene for big brother behavior carried by both big brother and littlebrother.

• Gene that makes big brother good to little brother may reappear moreoften because little brother carries an (unexpressed) copy of this gene.


Semi-Loving or Semi-Kantian?

• If alleles controlling actions in the two roles are close together onsame chromosome, so crossover is rare, then equilibria are symmetricNash equilibria of the semi-Kantian function.

• If alleles controlling actions in the two roles are unlinked, thenequilibria are symmetric Nash equilibria of the inclusive fitness“semi-loving” function.


Documents

Ethics, Evolution, and Games among Family and Neighborsecon.ucsb.edu/~tedb/Lectures/Brentalk.pdf · Ethics, Evolution, and Games among Family and Neighbors Ted Bergstrom April, 2009