The Social Gene vs. the Selfish Gene

1. The Social Gene vs. the Selfish Gene Is it in One’s Interest to Act for the Whole? Wayne Eastman weastman@business.rutgers.edu [v. 1.0—preliminary results—comments welcome] Rutgers Business School-Newark and New Brunswick

2. A beta version… There’s lots I could include in this ppt… Nods to impt sources… Reflections on what it all means—if the social gene beats the selfish gene, does it mean the teleology of Socrates, Plato, Aristotle, and Aquinas is back?; what are the implications for business, and for SCM in particular?; etc. This is a stripped-down, model-only version… A major reason is that the results presented here are preliminary, and close… On further review, they may change…

3. The basic question Suppose evolution consists of a random selection of one-shot, 2 x 2, two-player games. How does a “social gene” (S) that plays a highest joint value strategy (HJV) for the players fare in its reproductive success relative to a “selfish gene” (AKA a “non-social gene,” or N) that plays dominant strategies when applicable, and mixed Nash strategies otherwise?

4. The basic question, restated Maybe nature/evolution has designed genes so that they, and other evolved things, follow the same basic approach, either social or non-social, in all games… Which approach, social or non-social, does better for the gene (or person, or hyena, or bacterium) that follows it in games with other Ss and Ns?

5. My intuition about our intuitions Most of us think, I think, that the social gene will not do as well as the non-social gene. We intuit that the social gene will do better in games with other Ss than the non-social gene will do in games with another Ns, and that the non-social gene will do better than the social gene in their games together. As we will see, these intuitions are all correct. But do they add up to N winning overall?

6. My suspicion Maybe the intuition that N wins overall is wrong. Maybe we’re overly influenced by the Prisoner’s Dilemma. If we analyze all one-shot games, including all possible ordinal rankings in 2 x 2 matrices, assuming them all to be equally probable, maybe S doesn’t do so badly. Maybe S will even win.

7. The PD and other games In the PD, HJV is dominated. In what we can call Harmony games, in which HJV is dominant, S and N do equally well. The chance for S to equal or beat N in a one-shot, all-games tournament lies in Stag Hunt, Battle of the Sexes, and Chicken. In these games, S may do as well or better than N, taking into account within-group as well as cross-group games.

8. 144 Matrices This ppt analyzes each of the 144 2 x 2 matrices that are possible with ordinal rankings for the two players of 3 (best) to 2 (second best) to 1 (third best) to 0 (worst). The matrices are classified by whether HJV is unique and by what it is (3-3, 3-2, 2-3, 3-1, 1-3, or 2-2). The results for S and N as both Row and Column are shown for each matrix.

9. Four canonical matrices A reason to suspect that the conventional wisdom is right and N will win: In the canonical matrices of the PD (#137), Stag Hunt (#32), Chicken (#101), and Battle of the Sexes (#45) taken together, N beats S, even assuming (as I do) that S genes but not N genes apply Schelling focal point * cues to achieve HJV in the Battle of the Sexes. *S can also stand for Schelling, Socrates, or Sharing; N can also stand for Nash.

10. The canonical matrices, continued N beats S overall in the four canonical matrices because the big N lead in the PD is supplemented by a smaller N lead in Chicken. The two games in which N wins overcome the substantial S lead in the Stag Hunt and the smaller S lead in Battle of the Sexes.

11. A nuance or three on S In addition to assuming that S players converge on focal points, I assume the following in my model: • S preferentially plays HJV strategies that are dominant, or best responses to dominant strategies; • If there is no risk of losing HJV, S plays HJV strategies with higher individual payoffs for himself;

12. Nuances continued 3) When there is no HJV (the 6 zero-sum games, matrices #139-144), S plays mixed Nash.

13. A teaser One of the four major types of game behaves differently in the 17 matrices that exemplify it from the way it does in its canonical matrix. If you want to peek to see which game that is, and who wins overall, and game by game, go to the end…

14. Matrix #1--HarmonyC Matrix #1 Matrix #1 Matrix #1 Matrix #1 Matrix #1 R Matrix #1

15. Matrix #1—Analysis Type of game: Harmony I is DOM for R, i is DOM for C S, S = 3, 3 N, N = 3, 3 S, N = 3, 3 S, N two-game total = 6, 6

16. Matrix #2--Harmony C R

17. Matrix #2—Analysis Type of game: Harmony I is DOM for R, i is BR for C S, S = 3, 3 N, N = 3, 3 S, N = 3, 3 S, N two-game total = 6, 6

18. Matrix #3--Harmony C R

19. Matrix #3—Analysis Type of game: Harmony I is DOM for R, i is DOM for C S, S = 3, 3 N, N = 3, 3 S, N = 3, 3 S, N two-game total = 6, 6

20. Matrix #4 --Harmony C R

21. Matrix #4—Analysis Type of game: Harmony I is DOM for R, i is BR for C S, S = 3, 3 N, N = 3, 3 S, N = 3, 3 S, N two-game total = 6, 6

22. Matrix #5--Harmony C R

23. Matrix #5—Analysis Type of game: Harmony I is DOM for R, i is DOM for C S, S = 3, 3 N, N = 3, 3 S, N = 3, 3 S, N two-game total = 6, 6

24. Matrix #6--Harmony C R

25. Matrix #6—Analysis Type of game: Harmony I is DOM for R, i is BR for C S, S = 3, 3 N, N = 3, 3 S, N = 3, 3 S, N two-game total = 6, 6

26. Matrix #7--Harmony C R

27. Matrix #7—Analysis Type of game: Harmony I is DOM for R, i is DOM for C S, S = 3, 3 N, N = 3, 3 S, N = 3, 3 S, N two-game total = 6, 6

28. Matrix #8--Harmony C R

29. Matrix #8—Analysis Type of game: Harmony I is DOM for R, i is BR for C S, S = 3, 3 N, N = 3, 3 S, N = 3, 3 S, N two-game total = 6, 6

30. Matrix #9--Harmony C R

31. Matrix #9—Analysis Type of game: Harmony I is DOM for R, i is DOM for C S, S = 3, 3 N, N = 3, 3 S, N = 3, 3 S, N two-game total = 6, 6

32. Matrix #10--Harmony C R

33. Matrix #10—Analysis Type of game: Harmony I is DOM for R, i is BR for C S, S = 3, 3 N, N = 3, 3 S, N = 3, 3 S, N two-game total = 6, 6

34. Matrix #11--Harmony C R

35. Matrix #11—Analysis Type of game: Harmony I is DOM for R, i is DOM for C S, S = 3, 3 N, N = 3, 3 S, N = 3, 3 S, N two-game total = 6, 6

36. Matrix #12--Harmony C R

37. Matrix #12—Analysis Type of game: Harmony I is DOM for R, i is BR for C S, S = 3, 3 N, N = 3, 3 S, N = 3, 3 S, N two-game total = 6, 6

38. Matrix #13--Harmony C R

39. Matrix #13—Analysis Type of game: Harmony I is DOM for R, i is DOM for C S, S = 3, 3 N, N = 3, 3 S, N = 3, 3 S, N two-game total = 6, 6

40. Matrix #14--Harmony C R

41. Matrix #14—Analysis Type of game: Harmony I is DOM for R, i is BR for C S, S = 3, 3 N, N = 3, 3 S, N = 3, 3 S, N two-game total = 6, 6

42. Matrix #15--Harmony C R

43. Matrix #15—Analysis Type of game: Harmony I is DOM for R, i is DOM for C S, S = 3, 3 N, N = 3, 3 S, N = 3, 3 S, N two-game total = 6, 6

44. Matrix #16—Stag Hunt N S

45. Matrix #16—Analysis Type of game: Stag Hunt S, S = 3, 3 MNC = ¾ ii N, N = 1.5, 1.5 S, N = 1.5, 2.25 S, N two-game total = 4.5, 3.75

46. Matrix #17--Harmony C R

47. Matrix #17—Analysis Type of game: Harmony I is DOM for R, i is DOM for C S, S = 3, 3 N, N = 3, 3 S, N = 3, 3 S, N two-game total = 6, 6

48. Matrix #18--Harmony C R

49. Matrix #18—Analysis Type of game: Harmony I is DOM for R, i is BR for C S, S = 3, 3 N, N = 3, 3 S, N = 3, 3 S, N two-game total = 6, 6

50. Matrix #19--Harmony