A New Approach to Game Theory
Wayne Eastman
Supply Chain Management Seminar
September 11, 2015
In the Beginning: The Limits of
Rationality
Thomas Schelling
John Forbes Nash
The 1950s: The Prisoner’s Dilemma is a Bear
Strategy
i
Strategy
I
Strategy
II
2
3
Strategy
ii
2
3
0
0
1
1
The 1980s: Tit for Tat Wins in the
Iterated Dilemma
WWI Christmas Truce
Robert Axelrod
William Hamilton
An Optimistic Four Temperaments Approach to
Game Theory:
Sanguine, Choleric, Phlegmatic, and Melancholy Sub-Selves
Help People, Businesses, and All Players Solve Social Games
Three Propositions of the New Approach
1) 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.
2) 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.
3) 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.
Prop. 1: The Social Gene Beats the Selfish Gene
[Preliminary result…further analysis is required!]
E.O. Wilson—
Sociobiology (1975)
The logic of evolution is social…
Richard Dawkins—
The Selfish Gene (1976)
The logic of evolution is selfish…
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
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.
#144
Strategy
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Strategy
II
Strategy
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3
1
Strategy
ii
0
3
0
2
1
2
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.
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
2, 2
3, 0
3, 0
1, 1
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”
3, 3
1, 0
0, 1
2, 2
The Battle of the Sexes is Pretty Big for the
Social Player
• In the BOTS game below, two Social players get 2, 3, two NonSocials 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
2, 3
1, 2
0, 0
3, 1
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
3, 2
1, 3
0, 0
3, 1
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.
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.
Prop. 3: We Can Open the Door to Sanguine Reason
Okay! But how about being Socrates satisfied?! That’s the
best, no!?
The PD: Flip 1
Turning a Slacking Story into a Deference Story
The PD: Flip 2
Turning “Dishonesty” into “Agreeableness”
Harmony: Flip 3
Turning “Idiots!” into “I Get It!”
Harmony: Flip 4
Turning Respect into Love