Game Strategy in Biblical Times

Genesis 20:1-18 tells of Abraham visiting Avimelech and offering him Sarah (who, so Abraham tells Avimelech, is his sister, when she is also his wife). Despite Avimelech’s ignorance of the true relation between Abraham and Sarah, and despite the fact that he hasn’t slept with Sarah, G-d is angry at him and renders the women of his household sterile. G-d asks Avimelech to free Sarah. Presumably, the men in Avimelech’s household are not happy about their wives’ infertility, which causes Avimelech trouble.

Avimelech’s and G-d’s strategies seem described by the?payoff bi-matrix:

Avimelech does not have a?dominant strategy, nor does G-d.? But G-d doesn’t play strategies – he gets what he wants from people and causes them to do the right thing.? Avimelech knows this too.?Knowing that G-d will make the women in his household fertile again if he frees Sarah, and knowing that his best position is freeing her and having fertile women in the household, he does so.? (Free, Fertile) is a?Nash equilibrium, and all ends well.

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  1. William says:

    God. I just had to get that off my chest.

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  2. Trey says:

    The more interesting thing about this is why do you choose to bleep out the word God? Especially when you’re talking about the Bible.

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  3. Ian Kemmish says:

    Avimelech’s situation is a lot worse than that.

    The Abrahamic deity is concerned only with obedience, not with anything else. Just as Avimelech reaches the decision to free Sarah, having deduced that this constitutes obedience to the A.d.’s wishes, the A.d. could very well change its mind and punish him for freeing her instead of keeping her. Not being one of the bunch of randomly selected Israelite prophets, Avimelech has no way of knowing.

    There are many examples of this (Henry VIII got a lot of mileage out of one of them), but the starkest is how, at one point, the Israelites are commanded never to make graven or molten images, and then only a few years later, still in the desert, ordered to make brazen serpents and worship them.

    As the old saying goes: “You can’t win. You can’t break even. You can’t even quit the game.”

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  4. Shrey Goyal says:

    Referring to the Biblical entity as “G-d”: Ah! The mark of genius!

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  5. AaronS says:

    Professor,

    I don’t know if everyone understands that our Jewish brethren, out of respect to the Almighty, choose not to spell His Name completely. I hope you will pardon me, a Christian, for proceeding as we normally do.

    You will recall, no doubt, that Sarah WAS Abraham’s sister–his half-sister (I think of the same father). So he told a little half-truth in order to save himself.

    One “game theory” that I thought was well played was when King David sinned. God offered the Hobbesian choices of 3 years of famine, 3 years of decimating war, or days of “the sword of the Lord.”

    Instead of making a choice, David threw himself at the mercy of God, taking the third choice by saying, (1 Chr 21:13 KJV) “…let me fall now into the hand of the LORD; for very great are his mercies: but let me not fall into the hand of man.”

    And from the account, apparently God stopped his punishments before it was completely fulfilled–or at least there was indeed some element of mercy extended.

    Maybe the thing we can learn for game theory is that there may be some way to choose “beyond” the choices given…that gives a more positive outcome.

    In any case, an enjoyable read.

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  6. emw says:

    He’s probably Jewish, and doesn’t want to use the name of the supreme being. He’s using the Bible instead of the Torah recognizing his reader is more likely to be acquainted with the Bible, even though this story is in the common part of the two. It makes sense to me.

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  7. Syd says:

    Where is the part where God causes people to do the right thing? It sounds like Avimelech was lied to and innocent woman and men were punished. Why did Abraham offer his wife? I assume it was some kind of trade. If it was a trade did Abraham give back what he got in exchange?

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  8. Chris Falter says:

    I and probably many other readers do not know how to interpret the numbers in the payoff bi-matrix. Could someone kindly provide a link to an explanatory page?

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