A New Approach to Game Theory Wayne Eastman Supply Chain Management Seminar

1. A New Approach to Game TheoryWayne EastmanSupply Chain Management Seminar September 11, 2015

2. In the Beginning: The Limits of Rationality Thomas Schelling John Forbes Nash

3. The 1950s: The Prisoner’s Dilemma is a Bear

4. The 1980s: Tit for Tat Wins in the Iterated Dilemma WWI Christmas Truce Robert Axelrod William Hamilton

5. An Optimistic Four Temperaments Approach to Game Theory:Sanguine, Choleric, Phlegmatic, and MelancholySub-Selves Help People, Businesses, and All Players Solve Social Games

6. Three Propositions of the New Approach • The Social Gene Beats the Selfish Gene—In the universe of 2 x 2 one-shot games with ordinal utility and unknown types, a social player playing Highest Joint Value (HJV) narrowly prevails over a non-social player playing dominant strategies and best response to dominance where applicable, and mixed Nash otherwise. • Phlegmatic Business Ethics Is the Ascendant Ethic of Our Times—Choleric Warrior Ethics, Melancholy Priestly Ethics, and Phlegmatic Business Ethics all prevail over an egoist in the universe of one-shot 2x2 games with known types, with the business ethics player doing the best of all the types. • We Can Open the Door to Sanguine Reason—By assuming players with pro-social motivations, we can supplement Phlegmatic, Choleric, and Melancholy reason with Sanguine reason in our business and our personal lives.

7. Prop. 1: The Social Gene Beats the Selfish Gene[Preliminary result…further analysis is required!] E.O. Wilson— Richard Dawkins— Sociobiology (1975) The Selfish Gene (1976) The logic of evolution is social… The logic of evolution is selfish…

8. Q. Why Does Social Play Beat Non-Social Play, Assuming Unknown Types?A. Non-Prisoner’s Dilemma Games—Stag Hunts, Battles of the Sexes, and Chicken Games-- Narrowly Outweigh or “Outvote” Dilemmas The Stag Hunt The Battle of the Sexes Chicken

9. To see whether social or selfish (aka, non-social) wins, we need to analyze 144 2 x 2 matrices…In most of the matrices, like #1 and #144 below, the two strategies tie.

10. Harmony Rules, Most of the Time In 93 of the 144 matrices, the logic of Dominance followed by the non-social player N and the logic of Highest Joint Value followed by the social player S converge. These are “Harmony Games.” In all of them, the Social and Non-Social players do equally well.

11. The PD is Very Big for the Non-Social Player • In the classic PD below, two Social players get 2, 2, two Non-Socials get 1, 1, and N gets 3 and S 0 when they play together, for an N total of 4 and an S total of 2. This matrix is tied for worst for S among the 15 PDs, but is roughly representative. The PD is very strong for N. Matrix #137—Canonical PD

12. The Stag Hunt is Big for the Social Player • In the Stag Hunt below, two Social players get 3, 3, two Non-Socials get 1.5, 1.5, and S gets 1.5 and N .75 when they play together, for an S total of 4.5 and an N total of 2.25. That result is the best S gets in the 9 Stag Hunts, but it’s generally representative. The Stag Hunt is a strong game for Social. Matrix #24—Stag Hunt variant--AKA “Schelling”

13. The Battle of the Sexes is Pretty Big for the Social Player • In the BOTS game below, two Social players get 2, 3, two Non-Socials get 1.5, 1.5, and S gets 1.5 and N 1.75 when they play together, for an S total of 4 and an N total of 3.25. That result is average for S in the 8 BOTS matrices. The Battle of the Sexes is a good game for Social. Matrix #84—BOTS variant

14. The Surprise—Chicken is a Narrow Win for the Social Player • In the Chicken game below, two S players get 3, 2, two Ns get 1.5, 1.5, and S gets 1.5 and N 2.25 when they play together, for an S total of 4.5 and an N total of 4.25. Of the 17 Chicken matrices, S wins in 7, N in 3, and 7 are tied; overall, there is a narrow edge for Social. That allows S to pull out a narrow overall win in all 144 matrices. Matrix # 59—Chicken variant

15. Prop. 2: Choleric Warrior Ethics, Melancholy Priestly Ethics,Phlegmatic Business Ethics:They All Beat the Egoist in Games with Known Types Why the ethical types win: • The ethical types can commit; the egoist can’t; • The Warrior fights in the PD and avoids losing there; • The Priest punishes in the PD and avoids losing there; • The Manager, unlike the other types, persuades the egoist some of the time that what the Manager wants is in accord with what the egoist’s future self wants. • Business ethics is the winner in my model—and perhaps in our time.

16. How Ethical Types Solve a PD The Phlegmatic self “says”: • If the other player’s Sanguine side is in control, cooperating is dominant for her; • If the other player’s Choleric side is in control, neither strategy is dominant (because anger at oneself—guilt—is part of the Choleric); • So cooperation by the other is likely. • My Phlegmatic, self-interested side—“me”--says defect—but if I do, it’s likely my Melancholy and/or Choleric sides are going to make me feel like a louse for doing that; • Also, the Choleric side of the other player might come after me; • Also (if applicable)—the other player is one of those business ethics, work hard types who might be more in touch with my future self than I am myself.

17. Prop. 3: We Can Open the Door to Sanguine Reason Okay! But how about being Socrates satisfied?! That’s the best, no!?

18. The PD: Flip 1 Turning a Slacking Story into a Deference Story

19. The PD: Flip 2Turning “Dishonesty” into “Agreeableness”

20. Harmony: Flip 3Turning “Idiots!” into “I Get It!”

21. Harmony: Flip 4Turning Respect into Love