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Is God Rational?

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

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Is God Rational?

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  1. Is God Rational? Investigating the Application of Game Theory to The Old Testament Marlene M. Merchain Senior Capstone 2005 Advisor : Dr. Karrolyne Fogel

  2. ??? 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?

  3. 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.

  4. Background/BasicDefinitions • 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).

  5. Background/BasicDefinitions(cont’d) • 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.)

  6. Games To Be Examined • 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. 

  7. Adhere to Constraints (B) Don’t Adhere to Constraints (B’) Impose Constraints (A) Don’t Impose Constraints (A’) Game #1: Adam & Eve Outcome Matrix Adam and Eve God Key: (x,y)=(God, Adam and Eve) 4 = best ; 3 = next best ; 2 = next worst ; 1 = worst

  8. Adhere to Constraints (B) Don’t Adhere to Constraints (B’) Impose Constraints (A) Don’t Impose Constraints (A’) Game #1: Adam & Eve Outcome Matrix Analysis Adam and Eve Our outcome AB’is an equilibrium point! AB’ is the highest ‘x’ in its column and highest ‘y’ in its row God Key: (x,y)=(God, Adam and Eve) 4 = best ; 3 = next best ; 2 = next worst ; 1 = worst

  9. Some Strategies & Tools for Determining Rationality • Dominant Strategy- strategy Cdominates a strategy D if and only if every outcome in C is greater than its corresponding outcome in D.Cdominates D. • Dominance Principle- arational 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.

  10. Conclusions from Adam and Eve Game • Game Theory Outcome: God imposes constraints, Adam and Eve don’t adhere • Biblical Outcome: God imposes constraints, Adam and Eve don’t adhere Determination: God acts Rationally in Adam & Eve Game Result: Expulsion from Eden

  11. Pursue (B) Don’t Pursue (B’) Help Israelites (A) Don’t Help Israelites (A’) Game #2: Pharaoh Outcome Matrix Pharaoh *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 God Key: (x,y)=(God, Pharaoh) Security levels can help us out!

  12. Conclusions from Pharaoh Game • 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 Determination: God acts as Rational as possible in the Pharaoh Game Result: Pharaoh Gets A Taste of God’s Power!

  13. Complies (Builds Ark) (B) Disobeys (Doesn’t Build Ark) (B’) Spares Noah (A) Destroys Noah (A’) Game #3: Noah Marlene’s Outcome Matrix Noah *Dominant strategy for Noah ** Equilibrium point is “Pareto optimal” God Key: (x,y)=(God, Noah)

  14. Conclusions from Noah Game • Game Theory Outcome: God spares Noah, Noah complies • Biblical Outcome: God spares Noah, Noah complies Determination: God acts Rationally in Noah Game Result: Noah and his loved ones remained safe during the flood

  15. Final Overview : • 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…

  16. God is Rational!

  17. Bibliography • 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) Availablehttp://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.

  18. Graphics Complements of: • 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/Panels/index.html • Biblical Games Book cover: http://www.amazon.com/exec/obidos/tg/detail/-/0262523329/102-7691842-8123321?v=glance

  19. Offer Isaac (A) Don’t Offer Isaac (A’) Renege/ Relent (B) Renege/ Relent (B’) Game #3: Abraham Game Bram’s Outcome Matrices *Renege- To fail to carry out a promise or commitment: Abraham God 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

  20. Offer Isaac (A) Don’t Offer Isaac (A’) Renege (B) Don’t Renege (B’) Game #4: Abraham Game Brams’ 4a Outcome Matrix Abraham a) Abraham faithful regardless: prefers “offer” over “don’t offer” God Key: (x,y)=(God, Abraham)

  21. Offer Isaac (A) Don’t Offer Isaac (A’) Renege (B) Don’t Renege (B’) Game #4: Abraham Game Brams’ 4b Outcome Matrix Abraham b) Abraham wavers somewhat: prefers God “renege/relent” over “don’t renege/relent” God Key: (x,y)=(God, Abraham)

  22. Game #4: Abraham Game Brams’ 4c Matrix Analysis Abraham Offer Isaac (A) Don’t Offer Isaac (A’) c) Abraham wavers seriously: Isaac’s life paramount—same as (b) except if God adamant, would prefer “don’t offer” Renege/ Relent (B) God Don’t Renege/ Don’t Relent (B’) Key: (x,y)=(God, Abraham)

  23. Conclusions from Abraham Game • Game Theory Outcomes: a. b. c. • Biblical Outcome: Abraham sacrifices Isaac, God spares Isaac Determination: God acts Rationally in Abraham Game Result: Abraham rewarded by God for his faithfulness

  24. Mixed Strategy Of Pharaoh Game

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