a biblical game

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Game Theory Problems in the Old Testament

2010. Bifröst University

Miklos Erdei



A Biblical simultaneous game

Zagare (referring to Brams) give us an example

regarding to the Old Testament

Abraham sacrifice his son, Isaac to God

What controls Abraham’s decision to sacrifice his son?

1. Faith?

2. Rationality?



„Players”

Players in the game:

Abraham

God

Isaac definitely cannot seen as a playeras he has no possibilities to choose ormake any decision

Just a passive voice



What should Abraham do?

Abraham’s dilemma:

Show his loyalty to God

Save his son’s life

Abraham’s choices:

Obey God = Offer Isaac as a sacrifice

Disobey God = Save Isaac’s life and lose God’s mercy



What should Abraham do?

Abraham’s preferences: 3 assumptionsa. Abraham faithful regardless: Abraham prefers to offer

Isaac regardless of what God does subsequently

b. Abraham wavers somewhat: Abraham prefers that Godrelents regardless of what he does itself, however hewant to show God he still loyal

c. Abraham wavers seriously: If Abraham assumes that

God does not relent, he prefers not offer Isaac



What shall/would God say?

Cooperative strategy:

Reneging if Isaac were offered

Relenting if Abraham were disobeyed

Non-cooperative strategy:

Not reneging if Isaac were offered

Not relenting if Abraham were disobeyed



„Father, look, here is the fire and the wood, but

where is the lamb for burnt sacrifice?” (Isaac, Holy

Bible, Old Testament)



Payoff Matrix in the light of

Abraham’s assumption (a)

GOD

Renege/Relent(Cooperative)

Doesn’t

renege/relent(Non-cooperative)

ABRAHAMOffer Isaac

4

4

3

3

Doesn’t offer Issac

1

2

2

1




Abraham’s assumption (b)

GOD


Doesn’t


ABRAHAMOffer Isaac

4

4

3

2


1

3

2

1




Abraham’s assumption (c)

GOD


Doesn’t


ABRAHAMOffer Isaac

4

4

3

1


1

3

2

2



Consequences & Conclusions

Information assymetry among Abraham and God

God’s favor

Abraham has to make a decision while has no idea

what God planning to reply

If God plays cooperative then Isaac’s life is saved

If God decides to choose non-cooperative then

Isaac’s is gonna be sacrificed Isaac’s life depends on God choice (God’s reply

for Abraham’s strategy)




Under the condition of assumption (a):

Abraham has a dominant strategy (offer Isaacregardless God willing to do)

Under the condition of assumption (b): Theoretically Abraham has a dominant startegy altough

in a religious meaning has not

Under the condition of assumption (c): Abraham has no dominant either weak-dominant

strategy




The best outcome what they can get is (4;4) whenAbraham put forward to show his loyalty to God,instead of save Isaac’s life

If we assume that God begins to play „tit for tat”:

The best what Abraham could choose to offer Issac as asacrifice (the best possible outcome under theconditions of all assumptions)

This is the same „outcome” what the Bible tells us

occured in the Old Testament




Abraham’s assumption (a)

GOD


Doesn’t


ABRAHAMOffer Isaac

4

4

3

3


1

2

2

1



Bibliography

Zagare, Frank C. (1984). Game Theory. Concepts and applications. SAGE, New York, 47-51.

Avinash K. Dixit and Barry J. Nalebuff (1991).

Thinking strategically. Norton & Co. New York-London, pp. 57-58, 106-113.

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