Evolution of cooperation and fairness

Transcription

1 Evolution of cooeration and fairness What is cooeration? Martin Nowak Institute for Advanced Study, Princeton Donor ays a cost, c c < b Reciient gets a benefit, b Natural selection is based on cometition. How can natural selection lead to cooeration? Social insects Workers do not reroduce, but raise the offsring of another individual, the ueen. How can evolution design such altruistic behavior? Cooeration between relatives Hamilton s rule r > c / b Cooeration between relatives I jum into the river to save 2 brothers or 8 cousins J.B.S Haldane r coefficient of relatedness c cost of cooeration b benefit of cooeration 1

2 Evolutionary transitions reuire cooeration. Genes cooerate in a genome. Cells cooerate in an organism. Individuals cooerate in societies. How to get cooeration between non-relatives? The architecture of comlexity is based on cooeration. John von Neumann Oskar Morgenstern Game Theory Evolutionary game theory Successful strategies sread by natural selection. John Maynard Smith Prisoner s Dilemma Rational layers choose defection cooerate: C C - C 3 : 3 D - C 5 : 0 C - D 0 : 5 D - D 1 : 1 defect: D D - D 1 : 1 but cooeration would have been better for both: C - C 3 : 3 Cooeration is irrational. 2

3 Natural selection chooses defection 3 ossibilities for the evolution of cooeration DDCCDC DDDCDD DDDDDD CCCDDC CCDDDD DDDDDD CDCDCC CDDDCC DDDDDD Direct recirocity Indirect recirocity Satial recirocity D wins against C Direct recirocity Reeated Prisoner s Dilemma I hel you, but I exect we will meet again. Then you can hel me. Player 1 : C D C D C C C. Player 2 : D C D D C C C. Reeated Prisoner s Dilemma Player 1 : C D C D C C C. Player 2 : D C D D C C C. If you cooerate, then I will cooerate. If you defect, then I will defect. What is a good for the reeated Prisoner s Dilemma? Robert Axelrod Anatol Raaort 3

4 is too unforgiving Errors destroy cooeration : CCCCDCDCDCDDDDDD. : CCCDCDCDCDDDDDDD. Generous Generous If you cooerate, then I will cooerate. If you defect, then I will cooerate with robability 1/3. Never forget a good move. Sometimes forgive a bad move. 4

5 Generous Generous Always cooerate Generous Generous Always cooerate Always cooerate War and eace Win-stay, lose-shift Win-stay, lose-shift Exerimental observations Win - stay : C (3). C C Lose - shift : C (0). D D D (5). D C D (1). C D Manfred Milinski 5

6 Direct recirocity Indirect recirocity I hel you, you hel me. I hel you, somebody else hels me. Indirect recirocity Natural selection chooses donor reciient donor s reutation cooerate -c +b +1 defect strategies that base their decision to cooerate on the reutation of the reciient: hel those who have heled others Give and you shall receive. How it works: A rule for indirect recirocity You hel someone and increase thereby your reutation in society and the chance that you will receive hel. > c / b robability to know someone s reutation c cost of cooeration b benefit of cooeration 6

7 A universal constant of nature Another ossibility for the evolution of cooeration is the maximum fraction of eole who can be bad in the beginning such that everyone will be good in the end Satial game dynamics Cooerators Defectors Fairness Ultimatum Game $1,000,000 Prooser makes an offer. Ultimatum Game Ultimatum Game $1,000,000 $100 Prooser makes an offer. Resonder says yes or no. Prooser makes an offer. Resonder says yes or no. 7

8 What does game theory suggest? A rational resonder should refer $1 to $0. Therefore, a rational rooser should offer $1 and kee almost the whole sum. What do the exeriments show? Peole are not rational. Most roosers offer 30-50%. Most resonders reject offers below 30%. Evolutionary ultimatum Evolutionary ultimatum Strategies S(,) offer when rooser minimum accetance level when resonder Evolutionary ultimatum Strategies S(,) offer when rooser minimum accetance level when resonder Evolutionary ultimatum Strategies S(,) offer when rooser minimum accetance level when resonder The rational S(0,0) 8

9 Evolutionary ultimatum Evolutionary simulations Strategies S(,) offer when rooser minimum accetance level when resonder The fair S(1/2,1/2) The rational S(0,0) The rational S(0,0) Natural selection chooses low offers, low demands. It costs to reject offers, therefore low accetance levels are favored. If accetance levels decline, then offers will decline too. How can we exlain the evolution of fairness? Reutation! Evolutionary simulations Suose there is a chance that it will become known what offer a erson has acceted. Acceting low offers increases the robability of receiving reduced offers in the future. Rejecting low offers is costly, but buys the reutation of being someone who demands a fair share. The fair S(1/2,1/2) 9

10 Peole Karl Sigmund (Vienna) Karen Page (London) Robert May (Oxford) 10