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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.