## A doubt about Game Theory(Gibbons, Game Theory for Applied Economists) [closed]

When I read the book write by Robert Gibbons . In the first chapter, they discussed "The Problem of the Commons" I can't understand why

$v^{'} \left(g_i + g_{-i}^{*}\right)$ (page 27)

represent the damage of the price of the original price of the sheep.

I think the damage of the price of the original price should be:

$v \left(G\right) - v\left(g_i + g_{-i}^{*}\right)$

where $G$ means the original number of sheep . the price function $V$ has the relationship with the number of the sheep.

Also in the page 27, the author say the first order condition for this optimization problem

is $v \left(g_i + g_{-i}^{*}\right) + g_iv^{'} \left(g_i + g_{-i}^{*}\right) -c =0$

I can't understand the author want to say......Perhaps he means we should find $g_i$ as bigger as possible until we can't earn more money when we add more sheep.

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misleading title? also, question seems a bit localized, and I am not fond of questions which refer to something specific in a book without giving mor background or a link to a copy. – Yemon Choi Jul 1 2010 at 8:05
I have edited. thank you for your attention – Survivor Jul 1 2010 at 8:18
I think this question is in appropriate. Quite possibly there is a mistake in the book, but this is not the goal of MO. Perhaps a polite email to the author of the book could get an answer. – supercooldave Jul 1 2010 at 8:24
I don't think a question about an undergraduate economics textbook from someone having trouble finding the maximum of a smooth, strictly concave function is appropriate for MO. Nevertheless, the first part is simply the marginal effect of goats on v. For the second question, take the derivative of g_i v(G) with respect to g_i, set it equal to zero and you get the condition. – Michael Greinecker Jul 1 2010 at 8:28
Also, the title is somewhat misleading.... perhaps "doubt about game theory" is not the right phrase. – Willie Wong Jul 1 2010 at 10:34