Transcript Does It Pay To Be Greedy? - California Lutheran University

Is God Rational?
Investigating the Application of
Game Theory to The Old Testament
Marlene M. Merchain
Senior Capstone 2005
Advisor : Dr. Karrolyne Fogel
??? The Big Question ???
Is God rational, that is, when He
is a participant in a Biblical game,
does he act so that He may
benefit most from His decisions?
How Do We Determine If
God Is Rational?
God’s rationality will be determined by
performing a game theory analysis
on selected Biblical stories and
comparing the resulting outcomes to
the actual outcomes in the Bible.
Background/Basic Definitions
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Player- A participant in a situational event in which
decisions or “moves” are made.
Game- an interdependent decision situation whose
outcome depends on the choices of all players.
Move- when a player makes a choice among a
number of specified alternatives.
Payoffs (Utilities)- numerical values that are
assigned to ranked outcomes according to their level
of appeal to the player, (the higher the payoff, the
better the outcome).
Background/Basic Definitions (cont’d)
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Games of Perfect Information- games in which all
the choices of all the players are known to everyone
as soon as they are made.
Rational- given a player’s preferences and their
knowledge of the other players’ preferences, the
player makes strategical choices that would better
rather than worsen outcomes (outcomes that benefit
the player most.)
Games To Be Examined
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Games Predetermined By Brams:
 Adam & Eve Game
 Pharaoh Game
Game Created by Marlene:
 Noah Game
*To minimize confusion, games are referred to by God’s opponent. 
Game #1: Adam & Eve
Outcome Matrix
Adam and Eve
Adhere to
Constraints (B)
Adam and Eve
obedient,
God approving
Don’t Adhere to
Constraints (B’)
Adam and Eve
disobedient,
God disapproving
(3,2)
(2,3)
Don’t
Impose
Constraints
Adam and Eve
voluntarily
restrained,
God very pleased
Adam and Eve
unrestrained,
God very displeased
(A’)
(4,1)
(1,4)
Impose
Constraints
(A)
God
Key:
(x,y)=(God, Adam and Eve)
4 = best ; 3 = next best ; 2 = next worst ; 1 = worst
Game #1: Adam & Eve
Outcome Matrix Analysis
Adam and Eve
Adhere to
Constraints (B)
Impose
Constraints
God
(A)
Don’t
Impose
Constraints
Key:
(3,2)
(4,1)
(A’)
(x,y)=(God, Adam and Eve)
4 = best ; 3 = next best ; 2 = next worst ; 1 = worst
Don’t Adhere to
Constraints (B’)
(2,3)
(1,4)
Our outcome
AB’ is an
equilibrium
point!
AB’ is the highest
‘x’ in its column
and highest ‘y’ in
its row
Some Strategies & Tools for
Determining Rationality
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Dominant Strategy- strategy C dominates a strategy
D if and only if every outcome in C is greater than
its corresponding outcome in D. C dominates D.
Dominance Principle- a rational player should
never play a dominated strategy.
Saddle Point Principle- if a matrix game has a
saddle point (equilibrium point), both players should
play a strategy that contains it!
Security Level- the lowest guaranteed payoff a
player can attain.
Conclusions from Adam and Eve Game
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Game Theory Outcome:
God imposes constraints,
Adam and Eve don’t adhere
Biblical Outcome:
God imposes constraints,
Adam and Eve don’t adhere
Result: Expulsion from Eden
Determination:
God acts Rationally in Adam & Eve Game
Game #2: Pharaoh
Outcome Matrix
Pharaoh
Pursue
(B)
Don’t Pursue
(B’)
New
Confrontation
Help given
unnecessarily
(2,4)
(3,2)
Don’t Help
Israelites
Help
unforthcoming
Unaided flight
successful
(A’)
(4,1)
(1,3)
Help
Israelites
God
(A)
Key:
(x,y)=(God, Pharaoh)
Security levels can help us out!
*This game has
no pure
strategy
equilibrium!
The AB is
Pareto superior
A’B’, that is AB
is a better
outcome for
both players
than A’B’, but
not necessarily
the best for
either player
Conclusions from Pharaoh Game
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Game Theory Outcome:
No clear outcome…take your chances! However, if
both players play their security levels, the outcome is
God helps Israelites, Pharaoh pursues
Biblical Outcome:
God helps Israelites,
Pharaoh pursues
Result: Pharaoh Gets A Taste of
Determination:
God’s Power!
God acts as Rational as possible in the Pharaoh Game
Game #3: Noah
Marlene’s Outcome Matrix
Complies
(Builds Ark)
(B)
Noah
Disobeys
(Doesn’t Build Ark)
(B’)
Spares
Noah
God spares Noah,
Noah complies
God spares Noah,
Noah disobeys
(A)
(4,4)
(1,2)
Destroys
Noah
God destroys Noah,
Noah complies
God destroys Noah,
Noah disobeys
(A’)
(3,3)
(2,1)
God
Key:
(x,y)=(God, Noah)
*Dominant
strategy for
Noah
** Equilibrium
point is
“Pareto optimal”
Conclusions from Noah Game
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Game Theory Outcome:
God spares Noah,
Noah complies
Biblical Outcome:
God spares Noah,
Noah complies
Result: Noah and his loved ones
remained safe during the flood
Determination:
God acts Rationally in Noah Game
Final Overview :
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Game #1 vs. Adam & Eve- Plays Rationally
Game #2 vs. Pharaoh- As Rational as possible
Game #3 vs. Noah- Plays Rationally
So the final verdict is…
God is Rational!
Bibliography
1.
2.
3.
4.
5.
Brams, Steven J. Biblical Games: Game Theory and the Hebrew Bible.
Massachusetts: Massachusetts Institute of Technology, 2003.
McCain, Roger A. Game Theory: An Introductory Sketch. (Online)
Available http://william-king.www.drexel.edu/top/eco/game/game.html 30
November 2004.
Meeks, Wayne A, ed. The Harper Collins Study Bible. London: Harper
Collins Publishers, 1993
Rapoport, Anatol. Two-Person Game Theory. Mineola, New York:
Dover Publications, Inc., 1966
Straffin, Philip D. Game Theory and Strategy. Washington, D.C.: The
Mathematical Association of America, 1993.
Graphics
Complements of:
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Biblical Clip Art:
http://www.wels.net/wmc/html/clip_art_-_volume_2__part_a.html
Sistine Chapel Frescos:
http://sun.science.wayne.edu/~mcogan/Humanities/Sistine/Panel
s/index.html
Biblical Games Book cover:
http://www.amazon.com/exec/obidos/tg/detail//0262523329/102-7691842-8123321?v=glance
Game #3: Abraham Game
Bram’s Outcome Matrices
*Renege-
Abraham
To fail to carry out
a promise or
commitment:
Offer Isaac
(A)
Renege/
Relent
God
(B)
Renege/
Relent
(B’)
Don’t Offer Isaac
(A’)
Abraham faithful a. (4,4) Abraham faithful a. (3,3)
God merciful
b.(4,4) God adamant
b.(2,3)
Isaac saved
c. (4,4) Isaac sacrificed
c. (1,3)
Abraham resistant a.(2,1)
God merciful
b.(3,1)
Isaac saved
c. (3,1)
Abraham resistant a.(1,2)
God adamant
b.(1,2)
Isaac’s fate
c. (2,2)
uncertain
Key:
(x,y)=(God, Abraham) **Note: This matrix is a composition of 3 different matrices with 3
distinct views of Abraham’s possible mentalities toward this situation
Game #4: Abraham Game
Brams’ 4a Outcome Matrix
Abraham
Offer Isaac
(A)
Don’t Offer
Isaac (A’)
Renege
(B)
God
Don’t
Renege
(B’)
Key:
(x,y)=(God, Abraham)
(4,4)
(3,3)
a) Abraham faithful
regardless:
prefers “offer” over
“don’t offer”
(2,1)
(1,2)
Game #4: Abraham Game
Brams’ 4b Outcome Matrix
Abraham
Offer Isaac
(A)
Don’t Offer
Isaac (A’)
Renege
God
(B)
Don’t
Renege
(B’)
Key:
(x,y)=(God, Abraham)
(4,4)
(3,1)
(2,3)
(1,2)
b) Abraham wavers
somewhat:
prefers God
“renege/relent” over
“don’t renege/relent”
Game #4: Abraham Game
Brams’ 4c Matrix Analysis
Abraham
Offer Isaac
(A)
God
Renege/
Relent
(B)
Don’t Renege/
Don’t Relent
(B’)
Key:
(x,y)=(God, Abraham)
Don’t Offer Isaac
(A’)
c) Abraham wavers
(4,4)
(1,3)
(3,1)
(2,2)
seriously:
Isaac’s life
paramount—same as
(b) except if God
adamant, would prefer
“don’t offer”
Conclusions from Abraham Game
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Game Theory Outcomes:
a.
b.
c.
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Biblical Outcome:
Result: Abraham rewarded by God
for his faithfulness
Abraham sacrifices Isaac,
God spares Isaac
Determination:
God acts Rationally in Abraham Game
Mixed Strategy
Of Pharaoh Game