Game Theory 101: The Basics by William Spaniel

Author:William Spaniel [Spaniel, William]
Language: eng
Format: epub
Published: 2011-07-18T03:00:00+00:00

EUleft = EUright

(σup)(-3) + (σdown)(1) = (σup)(2) + (σdown)(0)

Although this may seem like a difficult task, note that σup and σdown must sum to one. That is, since we know player 1 only has two strategies, he must play down whenever he does not play up. Therefore, we can use the substitution σdown = 1 – σup to rewrite that equation as:

(σup)(-3) + (1 – σup)(1) = (σup)(2) + (1 – σup)(0)

And from there, all we need to do is solve for σup, and we will have our answer:

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